Robinson Tuition
Year 7 · Key Stage 3 · free KS3 maths worksheet

Angles

12 original questions, 38 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

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The questions

1

Here are three angles, p, q and r.

For each angle, write down whether it is acute, obtuse or reflex, and estimate its size in degrees.

pqr
3 marks
Show answer
p) acute, about 35° q) obtuse, about 120° r) reflex, about 250°
2

The diagram shows triangle PQR. One angle is marked.

  1. Use three letters to name the marked angle.
  2. Use two letters to name the longest side of the triangle.
  3. Use three letters to name the angle at vertex R.
  4. The side opposite angle P is called side p. Use two letters to name side p.
PQR
4 marks
Show answer
a) angle PQR (or RQP) b) PQ c) angle PRQ (or QRP) d) QR
3
  1. The diagram shows line AB above a ruler marked in centimetres and millimetres. Write down the length of AB to the nearest millimetre.
  2. Use a protractor to measure angle DEF.
ABDEF012345678910
2 marks
Show answer
a) 6.3 cm (63 mm) b) 137°
4
  1. At A, draw an angle of 65° above the line AB.
  2. At C, draw an angle of 270° measured anticlockwise from the line CD (a three-quarter turn).
ABCD
2 marks
Show answer
a) a line from A at 65° to AB b) a line from C straight down, making a reflex angle of 270° with CD
5

The grid is made of centimetre squares.

  1. Draw triangle ABC where AB = 6 cm, angle BAC = 90° and AC = 4 cm. C is above A.
  2. Measure angle ABC in your triangle.
AB
3 marks
Show answer
a) C is 4 squares directly above A; join C to B b) 34° (accept 32° to 36°)
6

Three angles meet at a point. Two of the angles are 145° and 118°. The third angle is x°.

Work out the value of x. Give a reason for your answer.

2 marks
Show answer
x = 97 (angles around a point add up to 360 degrees)
7

Two straight lines cross. One angle is 38°.

Work out the sizes of the angles marked a, b and c. Give a reason for each answer.

38°abcDiagram NOT accurately drawn
3 marks
Show answer
a) 38° (vertically opposite) b) 142° (angles on a straight line add up to 180°) c) 142° (vertically opposite to b)
8

Write down the mathematical name of each shape.

  1. A quadrilateral with four equal sides and four right angles.
  2. A quadrilateral with four equal sides and no right angles.
  3. A quadrilateral with exactly one pair of parallel sides.
  4. A quadrilateral with two pairs of equal sides next to each other, and one line of symmetry.
  5. A triangle with exactly two equal sides and two equal angles.
4 marks
Show answer
a) square b) rhombus c) trapezium d) kite e) isosceles triangle
9

Work out the sizes of the angles marked x, y and z.

48°75°x85°110°70°yzz40°Diagram NOT accurately drawn
4 marks
Show answer
x) 57° y) 95° z) 70°
10

ABC is a straight line. The point D lies above the line.

Triangle BCD is isosceles with BD = CD.

Angle DBA = 134°.

Work out the size of angle BDC. Give a reason for each stage of your working.

BCD134°ADiagram NOT accurately drawn
4 marks
Show answer
88°
11

In triangle ABC, the side BC is extended to D.

The angles inside the triangle are a, b and c. The angle outside the triangle at C is d.

  1. Explain why c + d = 180°
  2. Explain why a + b + c = 180°
  3. Use parts (a) and (b) to show that d = a + b
  4. When a = 50° and b = 65°, work out d.
BCAabcdDDiagram NOT accurately drawn
4 marks
Show answer
a) c and d lie on the straight line BCD b) angles in a triangle add up to 180° c) a + b + c = c + d, so a + b = d d) 115°
12

The diagram shows triangle ABC. The line PQ goes through C and is parallel to AB.

Alternate angles between parallel lines are equal.

  1. Explain why angle p = angle x.
  2. Explain why angle q = angle y.
  3. Use the straight line PQ to prove that x + y + z = 180°
ABxyzpqPQCDiagram NOT accurately drawn
3 marks
Show answer
a) alternate angles are equal b) alternate angles are equal c) p + z + q = 180° (straight line), and p = x, q = y, so x + y + z = 180°

Your score

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Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.

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