Measurement and Geometry P6 PSLE Mathematics

Angles

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Angles

Key Concepts

  • An angle is the amount of turn between 2 lines or rays that meet at a point.
  • The point where the 2 lines meet is called the vertex.
  • Angles are measured in degrees (°).

Types of angles

  • Acute angle: an angle less than 90°
  • Right angle: an angle exactly 90°
  • Obtuse angle: an angle more than 90° but less than 180°
  • Straight angle: an angle exactly 180°
  • Reflex angle: an angle more than 180° but less than 360°
  • Complete angle / full turn: an angle exactly 360°

Angles on a straight line

  • A straight line forms an angle of 180°.
  • If several angles lie along the same straight line, their total is 180°.
  • This helps us find a missing angle by subtraction.

Example idea:

  • If one angle is 65° on a straight line, the other angle is
    180° - 65° = 115°

Angles at a point

  • Angles around a point always add up to 360°.
  • This is because one complete turn is 360°.
  • If some angles around a point are known, the unknown angle can be found by subtracting the known angles from 360°.

Example idea:

  • If 3 angles at a point are 80°, 120° and 70°, the fourth angle is
    360° - (80° + 120° + 70°) = 90°

Vertically opposite angles

  • When 2 straight lines cross, they form 4 angles.
  • The angles directly opposite each other are called vertically opposite angles.
  • Vertically opposite angles are always equal.

Important facts:

  • If one angle is 50°, the angle opposite it is also 50°.
  • The 2 neighbouring angles will each be
    180° - 50° = 130°

Angles in a triangle

  • The 3 interior angles in any triangle always add up to 180°.

Special triangles

  • Right-angled triangle: has one angle of 90°
  • Isosceles triangle: has 2 equal sides and 2 equal angles
  • Equilateral triangle: has 3 equal sides and 3 equal angles
    • Each angle is 60° because
      180° ÷ 3 = 60°

How to find a missing angle:

  • Add the known angles
  • Subtract from 180°

Example idea:

  • In a triangle, if 2 angles are 45° and 65°, the third angle is
    180° - (45° + 65°) = 70°

Angles in quadrilaterals

  • A quadrilateral is a 4-sided shape.
  • The interior angles of any quadrilateral always add up to 360°.

Common quadrilaterals:

  • Square: 4 equal sides and 4 right angles
  • Rectangle: opposite sides equal and 4 right angles
  • Parallelogram: opposite sides parallel and equal
  • Rhombus: 4 equal sides
  • Trapezium / trapezoid: has one pair of parallel sides

How to find a missing angle:

  • Add the known angles
  • Subtract from 360°

Example idea:

  • In a quadrilateral, if 3 angles are 80°, 95° and 110°, the fourth angle is
    360° - (80° + 95° + 110°) = 75°

Finding unknown angles

To find unknown angles, use these angle facts:

  • Angles on a straight line = 180°
  • Angles at a point = 360°
  • Vertically opposite angles are equal
  • Angles in a triangle = 180°
  • Angles in a quadrilateral = 360°

Useful method:

  1. Look carefully at the diagram.
  2. Identify which angle rule applies.
  3. Write the angle fact clearly.
  4. Substitute the known values.
  5. Calculate the unknown angle.
  6. Check that the answer makes sense.

Important Definitions

  • Angle: the amount of turn between 2 lines or rays that meet at a point.
  • Degree (°): the unit used to measure angles.
  • Vertex: the point where 2 lines or rays meet to form an angle.
  • Straight line: a line that forms an angle of 180°.
  • Angles on a straight line: angles that add up to 180°.
  • Angles at a point: angles around one point that add up to 360°.
  • Vertically opposite angles: opposite angles formed when 2 straight lines cross; they are equal.
  • Triangle: a 3-sided shape.
  • Interior angles: angles inside a shape.
  • Quadrilateral: a 4-sided shape.
  • Isosceles triangle: a triangle with 2 equal sides and 2 equal angles.
  • Equilateral triangle: a triangle with 3 equal sides and 3 equal angles of 60° each.
  • Right angle: an angle of exactly 90°.
  • Acute angle: an angle less than 90°.
  • Obtuse angle: an angle more than 90° but less than 180°.
  • Reflex angle: an angle more than 180° but less than 360°.

Worked Examples

Example 1: Angles on a straight line

A straight line is divided into 2 angles. One angle is 128°. Find the other angle.

Solution

  1. Use the angle fact:
    Angles on a straight line add up to 180°
  2. Let the unknown angle be x.
  3. Write the equation:
    x + 128° = 180°
  4. Subtract 128° from 180°:
    x = 180° - 128°
  5. Calculate:
    x = 52°

Answer

52°

Example 2: Vertically opposite angles

Two straight lines cross. One of the angles is 74°. Find:

  • the angle vertically opposite it
  • one of the adjacent angles

Solution

  1. Use the angle fact:
    Vertically opposite angles are equal

  2. So the angle opposite 74° is also:
    74°

  3. Use the angle fact:
    Angles on a straight line add up to 180°

  4. Let the adjacent angle be x.

  5. Write the equation:
    74° + x = 180°

  6. Solve:
    x = 180° - 74° = 106°

Answer

  • Vertically opposite angle = 74°
  • Adjacent angle = 106°

Example 3: Angles in a quadrilateral

A quadrilateral has interior angles of 88°, 97°, 105° and x°. Find x.

Solution

  1. Use the angle fact:
    Angles in a quadrilateral add up to 360°
  2. Add the known angles:
    88° + 97° + 105° = 290°
  3. Subtract from 360°:
    x = 360° - 290°
  4. Calculate:
    x = 70°

Answer

70°

Common Mistakes to Avoid

  • Mixing up 180° and 360°
    • Straight line = 180°
    • Around a point = 360°
  • Forgetting that vertically opposite angles are equal
  • Adding angles wrongly due to careless arithmetic
  • Using the wrong shape rule
    • Triangle = 180°
    • Quadrilateral = 360°
  • Confusing adjacent angles with vertically opposite angles
  • Not checking whether the angle is inside the shape or outside it
  • Forgetting to write the degree symbol (°)
  • Assuming all triangles have equal angles
    • Only an equilateral triangle has three 60° angles
  • Misreading the diagram when lines are slanted
    • The angle facts stay the same even if the drawing is tilted

Exam Tips

  • Always write the angle fact first, such as:
    • Angles on a straight line add up to 180°.
    • Angles at a point add up to 360°.
    • Vertically opposite angles are equal.
    • Angles in a triangle add up to 180°.
    • Angles in a quadrilateral add up to 360°.
  • Show working clearly step by step. This helps you earn method marks.
  • Label the unknown angle as x if needed.
  • Circle or underline the angle you are finding.
  • If there are many angles, mark them neatly on the diagram.
  • Check if the answer is reasonable:
    • If it is on a straight line, the 2 angles should total 180°.
    • If it is in a triangle, all 3 angles should total 180°.
  • Be careful when a question uses more than one angle rule.
  • Use exact mathematical language, for example:
    • Therefore, x = 65°.
    • Hence, the unknown angle is 65°.

Quick Summary

  • An angle measures the amount of turn between 2 lines or rays.
  • Angles are measured in degrees (°).
  • Angles on a straight line add up to 180°.
  • Angles at a point add up to 360°.
  • Vertically opposite angles are equal.
  • The interior angles of a triangle add up to 180°.
  • The interior angles of a quadrilateral add up to 360°.
  • An equilateral triangle has 3 angles of 60° each.
  • To find an unknown angle, identify the correct angle rule first.
  • Show your working clearly and include the degree symbol.
  • Always check that your final answer fits the diagram.
  • Slanted diagrams do not change the angle facts.
✏️ 25 practice questions available

30 questions from school exam papers

Q1

In the figure, PQS is an isosceles triangle. PVS, QSR and TVR are straight lines and PQ = PS. ∠QPS = 46° and ∠TRQ = 17°. Find ∠y.

A triangle configuration showing: Triangle PQS at the top with P at the apex and base QS. Point T lies on PQ, point V lies on PS, and point R is to the right of S on the extended line. Angle at P is marked as 46°. Angle at R is marked as 17°. Angle y is marked at point T (or within the triangle). The angle at S is marked as 12°.
📊 Diagram: A triangle configuration showing: Triangle PQS at the top with P at the apex and base QS. Point T lies on PQ, point V lies on PS, and point R is to the right of S on the extended line. Angle at P is marked as 46°. Angle at R is marked as 17°. Angle y is marked at point T (or within the triangle). The angle at S is marked as 12°.
2022-P6-Maths-Prelim-ACSJ 2022
Q2

The figure below is not drawn to scale. DC and AEB are straight lines. AEB is parallel to DC. ∠FDA = 122° and ∠EBC = 58°. Each of the statements is either true, false or not possible to tell from the information given. For each statement, put a tick (✓) to indicate your answer. Statements to evaluate: 1. ∠EBC = ∠ECB 2. AECD is a trapezium. 3. ABCD is a parallelogram.

A geometric figure with points A, B, C, D, E, and F. Lines DC and AEB are straight lines with AEB parallel to DC. Point F is to the left, D is on line FC, C is at the bottom right, B is at the top right, A is at the top left, and E is between A and B. Angle FDA is marked as 122° and angle EBC is marked as 58°.
📊 Diagram: A geometric figure with points A, B, C, D, E, and F. Lines DC and AEB are straight lines with AEB parallel to DC. Point F is to the left, D is on line FC, C is at the bottom right, B is at the top right, A is at the top left, and E is between A and B. Angle FDA is marked as 122° and angle EBC is marked as 58°.
2022-P6-Maths-Prelim-ACSJ 2022
Q3

In the square grid below, PQ and QR are straight lines. Measure and write down the size of ∠PQR.

A square grid with points P, Q, and R marked. PQ and QR are straight lines forming an angle at Q. Point P is located on the left side of the grid, point Q is located above and to the right of P, and point R is located to the right of Q. The grid appears to be approximately 16 units wide and 12 units tall.
📊 Diagram: A square grid with points P, Q, and R marked. PQ and QR are straight lines forming an angle at Q. Point P is located on the left side of the grid, point Q is located above and to the right of P, and point R is located to the right of Q. The grid appears to be approximately 16 units wide and 12 units tall.
2022-P6-Maths-Prelim-ACSJ 2022
Q4

In the figure, not drawn to scale, ABCD is a square. ACE and DGA are equilateral triangles. Find ∠EFG.

A square ABCD with point A at bottom centre, B at bottom right, C at top right, and D at top left (implied). Triangle ACE is equilateral with E positioned to the left of the square. Triangle DGA is equilateral with G positioned at the bottom left. Point F appears to be the intersection of lines within the figure. Various line segments connect the vertices: AC, AE, EC, AD, DG, GA, AB, BC, and additional lines connecting these triangles.
📊 Diagram: A square ABCD with point A at bottom centre, B at bottom right, C at top right, and D at top left (implied). Triangle ACE is equilateral with E positioned to the left of the square. Triangle DGA is equilateral with G positioned at the bottom left. Point F appears to be the intersection of lines within the figure. Various line segments connect the vertices: AC, AE, EC, AD, DG, GA, AB, BC, and additional lines connecting these triangles.
3 marks
2022-P6-Maths-Prelim-ACSJ 2022
Q5

In the figure below, BCDE is a rhombus and AE = DE. ∠EBC = 38° and ∠ADE = 54°. Find ∠P.

A geometric figure showing a rhombus BCDE with point A above the rhombus and point E on the rhombus. Lines are drawn from A to D, A to E, and A to B. Point P is marked inside the figure where lines intersect. The angle at D is labeled 54° and the angle at B is labeled 38°.
📊 Diagram: A geometric figure showing a rhombus BCDE with point A above the rhombus and point E on the rhombus. Lines are drawn from A to D, A to E, and A to B. Point P is marked inside the figure where lines intersect. The angle at D is labeled 54° and the angle at B is labeled 38°.
2 marks
2022-P6-Maths-Prelim-ACSJ 2022
Q6

Shamsul was North-East of Teddy. At first, they were facing each other. Then both boys made the smallest turn to face North. Which of the following represents the turn made by each boy?

A compass diagram showing North (N) pointing upward with a vertical line and arrow.
📊 Diagram: A compass diagram showing North (N) pointing upward with a vertical line and arrow.
A. Shamsul: 135° anti-clockwise, Teddy: 45° clockwise
B. Shamsul: 135° clockwise, Teddy: 45° anti-clockwise
C. Shamsul: 45° anti-clockwise, Teddy: 135° clockwise
D. Shamsul: 45° clockwise, Teddy: 135° anti-clockwise
2022-P6-Maths-Prelim-Catholic_High 2022
Q7

ABCD is a rectangle. E and F are points on the rectangle. ∠ADF = 260° and ∠EDC = 60°. Find ∠EDF.

A rectangle ABCD with point E on side AB and point F on side BC. From vertex D, there are lines drawn to points E and F. Angles are marked at D: one showing 280° on the left side of line DE, and 60° marked between line DC and line DF.
📊 Diagram: A rectangle ABCD with point E on side AB and point F on side BC. From vertex D, there are lines drawn to points E and F. Angles are marked at D: one showing 280° on the left side of line DE, and 60° marked between line DC and line DF.
A. 20°
B. 30°
C. 45°
D. 50°
2022-P6-Maths-Prelim-Catholic_High 2022
Q8

Find the value of 6 ÷ 3/5

Diagram for question 17
1 mark
2022-P6-Maths-Prelim-Catholic_High 2022
Q9

In the figure, ABCD is a rhombus and AEB is an equilateral triangle. FBD and EFC are straight lines. ∠BDA = 79° and ∠FCB = 19°. Find ∠EFD.

A rhombus ABCD with point E above the rhombus forming an equilateral triangle AEB. Point F lies on line EC. The angle at D (∠BDA) is marked as 79°, and the angle at C (∠FCB) is marked as 19°. Lines FBD and EFC are drawn as straight lines through the figure.
📊 Diagram: A rhombus ABCD with point E above the rhombus forming an equilateral triangle AEB. Point F lies on line EC. The angle at D (∠BDA) is marked as 79°, and the angle at C (∠FCB) is marked as 19°. Lines FBD and EFC are drawn as straight lines through the figure.
3 marks
2022-P6-Maths-Prelim-Catholic_High 2022
Q10

WXYZ is a parallelogram. Find ∠XYV.

Parallelogram WXYZ with angle at W marked as 114°. Point V is located on side YZ, creating triangle or angle configuration with vertices W, X, Y, V, Z labeled.
📊 Diagram: Parallelogram WXYZ with angle at W marked as 114°. Point V is located on side YZ, creating triangle or angle configuration with vertices W, X, Y, V, Z labeled.
A. 57°
B. 66°
C. 48°
D. 33°
2022-P6-Maths-Prelim-Henry_Park 2022
Q11

In the square grid below, AB and BC are straight lines. (a) Measure and write down the size of ∠ABC. (b) AB and BC form two sides of a parallelogram ABCD. Complete the drawing of the parallelogram ABCD within the grid and label point D.

A square grid with two straight lines forming an angle at point B. Point B is marked with an angle symbol. Line AB goes from lower right to upper left direction. Line BC goes from point B to the right and slightly downward. Points A, B, and C are labeled on the grid.
📊 Diagram: A square grid with two straight lines forming an angle at point B. Point B is marked with an angle symbol. Line AB goes from lower right to upper left direction. Line BC goes from point B to the right and slightly downward. Points A, B, and C are labeled on the grid.
2 marks
2022-P6-Maths-Prelim-Henry_Park 2022
Q12

PQRS is a square. STR is an equilateral triangle. Find the value of ∠QPT.

A square PQRS with vertices labeled P (top left), Q (top right), R (bottom right), and S (bottom left). An equilateral triangle STR is formed with T inside the square, where S is the bottom left vertex of the square and R is the bottom right vertex of the square. Point T is above the line SR.
📊 Diagram: A square PQRS with vertices labeled P (top left), Q (top right), R (bottom right), and S (bottom left). An equilateral triangle STR is formed with T inside the square, where S is the bottom left vertex of the square and R is the bottom right vertex of the square. Point T is above the line SR.
2022-P6-Maths-Prelim-Henry_Park 2022
Q13

In the figure below, UVWX is a parallelogram and XYZ is an isosceles triangle where XY = XZ. UXY and WXZ are straight lines and the sum of ∠YZX and ∠XWV is 147°. Find ∠UVW.

A figure showing parallelogram UVWX with vertices V (bottom left), U (bottom middle), W (top left), and X (top middle). An isosceles triangle XYZ is drawn with X at the left vertex, Y at the top vertex, and Z at the right vertex. The parallelogram and triangle share vertex X. Lines UXY and WXZ are drawn as straight lines passing through X. WX is parallel to UV (sides of parallelogram), and XZ is parallel to VU.
📊 Diagram: A figure showing parallelogram UVWX with vertices V (bottom left), U (bottom middle), W (top left), and X (top middle). An isosceles triangle XYZ is drawn with X at the left vertex, Y at the top vertex, and Z at the right vertex. The parallelogram and triangle share vertex X. Lines UXY and WXZ are drawn as straight lines passing through X. WX is parallel to UV (sides of parallelogram), and XZ is parallel to VU.
3 marks
2022-P6-Maths-Prelim-Henry_Park 2022
Q14

The figure below shows angles at a point O. Without using a protractor, draw another angle at O which is the same size as ∠x in the figure below. Label the angle as y.

Multiple lines meeting at point O with an angle labeled x marked between two of the lines.
📊 Diagram: Multiple lines meeting at point O with an angle labeled x marked between two of the lines.
1 mark
2022-P6-Maths-Prelim-Henry_Park 2022
Q15

ABCD is a square and DEFG is a trapezium. AG and DH are straight lines. DG is parallel to EF. Find ∠x.

A composite figure showing square ABCD on the left with angles marked as 56° at B and 24° at D. Trapezium DEFG extends to the right. Lines AG and DH are straight lines passing through the figure. Point H extends to the right. Angles are marked: 56° at B, 24° at D, x at point F (or E), y at point H, and 82° near G.
📊 Diagram: A composite figure showing square ABCD on the left with angles marked as 56° at B and 24° at D. Trapezium DEFG extends to the right. Lines AG and DH are straight lines passing through the figure. Point H extends to the right. Angles are marked: 56° at B, 24° at D, x at point F (or E), y at point H, and 82° near G.
2022-P6-Maths-Prelim-Henry_Park 2022
Q16

ABCD is a square and AEFG is a rectangle. AB = 24 cm and GF = 30 cm. Point E lies on BC while Point D lies on FG. Find the length of AG.

A diagram showing three straight lines (AB, CD, and EF) intersecting at a point. Line CD makes an angle of 29° with line EB. An angle of 103° is marked between lines AF and AD. The angle ∠r is marked between lines EB and BD.
📊 Diagram: A diagram showing three straight lines (AB, CD, and EF) intersecting at a point. Line CD makes an angle of 29° with line EB. An angle of 103° is marked between lines AF and AD. The angle ∠r is marked between lines EB and BD.
2022-P6-Maths-Prelim-MGS 2022
Q17

Two identical semicircles and two identical quadrants are cut out from a square piece of grey paper as shown below. Taking π = 22/7,

Two diagrams showing an equilateral triangle before and after folding. The original triangle shows a 60° angle marked at the bottom left vertex. The folded diagram shows the result after folding along a dotted line, with a 61° angle marked and angle n marked at the top right, with another 60° angle marked at the bottom left.
📊 Diagram: Two diagrams showing an equilateral triangle before and after folding. The original triangle shows a 60° angle marked at the bottom left vertex. The folded diagram shows the result after folding along a dotted line, with a 61° angle marked and angle n marked at the top right, with another 60° angle marked at the bottom left.
A. 59°
B. 60°
C. 61°
D. 62°
2022-P6-Maths-Prelim-MGS 2022
Q18

ABC is an equilateral triangle and ADEF is a square. GAC is a straight line. Find ∠BAD.

A geometric figure showing point A at the center with multiple rays extending outward. Triangle ABC is equilateral with B at top right and C at bottom right. Square ADEF is formed with D and E at bottom right, F at bottom left. Point G is on the left side. An angle of 128° is marked at point A between rays AG and AF.
📊 Diagram: A geometric figure showing point A at the center with multiple rays extending outward. Triangle ABC is equilateral with B at top right and C at bottom right. Square ADEF is formed with D and E at bottom right, F at bottom left. Point G is on the left side. An angle of 128° is marked at point A between rays AG and AF.
2022-P6-Maths-Prelim-MGS 2022
Q19

ABCD is a rhombus and CDEF is a square. ∠BAD is 124°. Find ∠BFC.

A 3D geometric figure showing a rhombus ABCD and a square CDEF. Point A is at the left with an angle of 124° marked at ∠BAD. Points are labeled with A at top-left, B at bottom-left, C in the middle, D above C, E at top-right, and F at bottom-right. The rhombus ABCD and square CDEF share the edge CD.
📊 Diagram: A 3D geometric figure showing a rhombus ABCD and a square CDEF. Point A is at the left with an angle of 124° marked at ∠BAD. Points are labeled with A at top-left, B at bottom-left, C in the middle, D above C, E at top-right, and F at bottom-right. The rhombus ABCD and square CDEF share the edge CD.
2 marks
2022-P6-Maths-Prelim-MGS 2022
Q20

PSV is an isosceles triangle, PS = VS. RSTW is a rhombus. PT and RV are straight lines. ∠WPQ = 35° and ∠PSV = 32°. Find ∠TUS.

A geometric figure showing: Triangle PSV with P on the left, S at the bottom right, and V at the top. A rhombus RSTW with R at the bottom left, S at the bottom right, T at the right, and W at the top. Point Q is on line PR between P and R. Point U is on line PT between P and T. Angles marked: ∠WPQ = 35° at P, ∠PSV = 32° at S, and ∠SRW = 78° at R. Lines PT and RV are straight lines passing through the figure.
📊 Diagram: A geometric figure showing: Triangle PSV with P on the left, S at the bottom right, and V at the top. A rhombus RSTW with R at the bottom left, S at the bottom right, T at the right, and W at the top. Point Q is on line PR between P and R. Point U is on line PT between P and T. Angles marked: ∠WPQ = 35° at P, ∠PSV = 32° at S, and ∠SRW = 78° at R. Lines PT and RV are straight lines passing through the figure.
2 marks
2022-P6-Maths-Prelim-MGS 2022
Q21

AB and CD are straight lines. Which of the following is true?

A diagram showing two straight lines AB and CD intersecting at a point. Multiple angles are formed and labeled: w, x, y, z. Point A is at upper left, C is at upper right, B is at lower right, D is at lower left, and E is at the bottom. The angles w, x, y, z are marked around the intersection point.
📊 Diagram: A diagram showing two straight lines AB and CD intersecting at a point. Multiple angles are formed and labeled: w, x, y, z. Point A is at upper left, C is at upper right, B is at lower right, D is at lower left, and E is at the bottom. The angles w, x, y, z are marked around the intersection point.
A. ∠w = ∠x + ∠y
B. ∠x = ∠w + ∠x
C. ∠w + ∠x + ∠y = 180°
D. ∠x + ∠y + ∠z = 180°
2022-P6-Maths-Prelim-Nan_Chiau 2022
Q22

In the figure below, DFE and DFG are isosceles triangles. FD = FE = FG. ∠FDG = 36°. Find ∠FDE.

Two isosceles triangles sharing a common side DF. Triangle DFE is on the left with vertices D (top), E (bottom left), F (bottom right). Triangle DFG is on the right with vertices D (top), F (bottom left), G (bottom right). The angle at D marked as 36° is ∠FDG. Points E, F, G appear to be collinear on the base.
📊 Diagram: Two isosceles triangles sharing a common side DF. Triangle DFE is on the left with vertices D (top), E (bottom left), F (bottom right). Triangle DFG is on the right with vertices D (top), F (bottom left), G (bottom right). The angle at D marked as 36° is ∠FDG. Points E, F, G appear to be collinear on the base.
2022-P6-Maths-Prelim-Nan_Chiau 2022
Q23

Billy is facing the pond. Where will he be facing after he turns 135° anti-clockwise?

A square grid containing 7 columns and 7 rows. The grid shows the locations of: Library (top row, center-right), Market (top row, right), Billy's House (middle-left area), Billy (marked with a person icon, center area), Pond (center-right area), and School (lower-center area). A compass rose indicates North pointing upward.
📊 Diagram: A square grid containing 7 columns and 7 rows. The grid shows the locations of: Library (top row, center-right), Market (top row, right), Billy's House (middle-left area), Billy (marked with a person icon, center area), Pond (center-right area), and School (lower-center area). A compass rose indicates North pointing upward.
2022-P6-Maths-Prelim-Nan_Chiau 2022
Q24

The diagram below shows two parallelograms ABCD and ABGE. ∠AEG = 45° and ∠BCD = 60°. Find ∠ABG.

Two parallelograms ABCD and ABGE sharing side AB. Parallelogram ABCD has vertices A (top right), B (top left), C (bottom left), D (bottom right) with ∠BCD = 60° marked at C. Parallelogram ABGE has vertices A (top right), B (top left), G (middle left), E (middle right) with ∠AEG = 45° marked at E. Point F lies on segment GD. The angle at A in parallelogram ABGE is marked as 45°.
📊 Diagram: Two parallelograms ABCD and ABGE sharing side AB. Parallelogram ABCD has vertices A (top right), B (top left), C (bottom left), D (bottom right) with ∠BCD = 60° marked at C. Parallelogram ABGE has vertices A (top right), B (top left), G (middle left), E (middle right) with ∠AEG = 45° marked at E. Point F lies on segment GD. The angle at A in parallelogram ABGE is marked as 45°.
2022-P6-Maths-Prelim-Nan_Chiau 2022
Q25

PQRS is a parallelogram. TSR and QVU are straight lines. PST and SRU are isosceles triangles. PT = PS and SR = SU. Find ∠RSU.

A geometric figure showing parallelogram PQRS with points T, U, and V. Point S appears to be on line segment connecting vertices. Angle measurements shown: 68° at S (between lines TS and SP), 62° at R (between lines QR and RU), and 22° at U. TSR is a straight line passing through S. QVU appears to be another straight line. Triangle PST is isosceles with PT = PS. Triangle SRU is isosceles with SR = SU.
📊 Diagram: A geometric figure showing parallelogram PQRS with points T, U, and V. Point S appears to be on line segment connecting vertices. Angle measurements shown: 68° at S (between lines TS and SP), 62° at R (between lines QR and RU), and 22° at U. TSR is a straight line passing through S. QVU appears to be another straight line. Triangle PST is isosceles with PT = PS. Triangle SRU is isosceles with SR = SU.
1 mark
2022-P6-Maths-Prelim-Nan_Chiau 2022

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