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Grade 3 · Foundation · free GCSE maths worksheet

Angles on a line, around a point and vertically opposite

Angle facts and finding missing angles.

11 original questions, 24 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Write down the mathematical name for an angle that is greater than 90° but less than 180°.

1 mark
Show answer
obtuse
2

An angle has size 210°.

Write down the mathematical name for this type of angle.

1 mark
Show answer
reflex
3

Two angles on a straight line are 47° and p°.

  1. Work out the value of p.
  2. Write down the mathematical name for an angle of this size.
2 marks
Show answer
a) 133 b) obtuse
4

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
5

Two straight lines cross at a point. One of the four angles is 52°.

  1. Write down the size of the angle vertically opposite the 52° angle.
  2. Work out the size of one of the other two angles.
2 marks
Show answer
a) 52 b) 128
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
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x = 97 (angles around a point add up to 360 degrees)
7

Jamal says that angles of 130°, 95° and 125° can meet at a point.

Is Jamal correct? You must show your working.

2 marks
Show answer
No. 130 + 95 + 125 = 350, but angles around a point add up to 360 degrees
8

In triangle ABC, the point D lies on the side BC, so that BDC is a straight line. Angle ADB = 112° and angle DAC = 30°.

  1. Work out the size of angle ADC. Give a reason for your answer.
  2. Work out the size of angle ACD. Give a reason for your answer.
3 marks
Show answer
a) 68, angles on a straight line add up to 180 degrees b) 82, angles in a triangle add up to 180 degrees
9

AOB is a straight line. The point C lies above the line.

Angle AOC = 5x° and angle COB = (4x − 9)°.

Work out the value of x. Give a reason for each stage of your working.

ABOC5x°(4x − 9)°Diagram NOT accurately drawn
3 marks
Show answer
x = 21
10

Two straight lines cross. Two vertically opposite angles are (3x + 10)° and (5x − 20)°.

  1. Work out the value of x.
  2. Work out the size of an angle next to (3x + 10)°.
3 marks
Show answer
a) 15 b) 125
11

Four angles meet at a point. The angles are 3x°, 4x°, (x + 20)° and 100°.

  1. Work out the value of x.
  2. Give a reason for your method.
3 marks
Show answer
a) 30 b) angles around a point add up to 360 degrees

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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