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Year 8 · Key Stage 3 · free KS3 maths worksheet

Angles in parallel lines

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

The diagram shows triangle ABC.

  1. Use three letters to name the marked angle.
  2. Write down the side opposite the vertex A.
  3. Use three letters to name the angle between the sides AC and BC.
ABCDiagram NOT accurately drawn
3 marks
Show answer
a) ABC (or CBA) b) BC c) ACB (or BCA)
2

Two angles fit together on a straight line. One of the angles is 64° and the other angle is y°.

  1. Work out the value of y.
  2. Give a reason for your answer.
2 marks
Show answer
a) 116 b) angles on a straight line add up to 180 degrees
3

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)
4

The diagram shows two straight lines crossing.

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

38°abcDiagram NOT accurately drawn
3 marks
Show answer
a) 38° (vertically opposite angles are equal) b) 142° (angles on a straight line add up to 180°) c) 142° (vertically opposite to b)
5

The line AB is perpendicular to the line CD. They cross at O. The straight line EF also passes through O.

Angle BOE = 27°.

  1. Work out the size of angle x. Give a reason.
  2. Work out the size of angle y. Give a reason.
27°xyABCDEFODiagram NOT accurately drawn
3 marks
Show answer
a) 63° (AB and CD are perpendicular, so angle BOC = 90°) b) 63° (vertically opposite to x)
6

The diagram shows two parallel lines crossed by a straight line.

Work out the sizes of the angles a, b and c. For each one, give a reason.

65°abcDiagram NOT accurately drawn
4 marks
Show answer
a) 65° (alternate angles are equal) b) 65° (corresponding angles are equal) c) 115° (co-interior angles add up to 180°)
7

The diagram shows two parallel lines crossed by a straight line.

One of the marked angles is 71°. The angle marked x° is the co-interior angle between the parallel lines on the same side of the crossing line.

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

71°x°Diagram NOT accurately drawn
3 marks
Show answer
x = 109 (co-interior angles between parallel lines add up to 180 degrees)
8

The diagram shows two parallel lines crossed by a straight line. Two of the angles are marked.

  1. Write down why (3x − 10)° = (2x + 25)°.
  2. Work out the size of each marked angle.
(3x - 10)°(2x + 25)°Diagram NOT accurately drawn
3 marks
Show answer
a) They are alternate angles, and alternate angles are equal b) 95°
9

AB and CD are parallel straight lines.

A straight line crosses AB at E and crosses CD at F. On line AB, A is to the left of E and B is to the right of E. On line CD, C is to the left of F and D is to the right of F.

Angle AEF = 62°.

Work out the size of angle CFE.

Give a reason for each stage of your working.

62°ABCDEFDiagram NOT accurately drawn
4 marks
Show answer
118°
10

DE and FG are parallel straight lines.

Triangle ABC is drawn so that A lies on DE, and B and C both lie on FG.

D is to the left of A and E is to the right of A.

Angle DAB = 48° and angle ACB = 63°.

Work out the size of angle BAC.

Give a reason for each stage of your working.

48°63°ABCDEFGDiagram NOT accurately drawn
4 marks
Show answer
69°
11

A straight line crosses line AB at the point P and crosses line CD at the point Q, where P is above Q. On line AB, B is to the right of P. On line CD, D is to the right of Q.

Angle QPB, between PQ and PB and inside the region between the two lines, is 104°.

Angle PQD, between QP and QD and inside the region between the two lines, is 76°.

Show that AB is parallel to CD.

Give reasons for your answer.

104°76°ABCDPQDiagram NOT accurately drawn
4 marks
Show answer
104° + 76° = 180°; angle QPB and angle PQD are co-interior angles; co-interior angles adding to 180° means the lines are parallel
12

The diagram shows triangle ABC. The line DAE is drawn through A, parallel to BC.

The angles of the triangle are p, q and r.

Show that p + q + r = 180°. Give a reason for each step.

ABCpqrDEDiagram NOT accurately drawn
3 marks
Show answer
Angle DAB = p and angle EAC = q (alternate angles), and DAB + r + EAC = 180° (angles on a straight line), so p + q + r = 180°

Your score

Answer the questions above and your score appears here.

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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