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Angles

Angles on a straight line add to 180°

Example 1: Find the size of angle a

angles 1

Angles on a straight line add to 180°
a + 130° = 180°
a = 50°

Example 2: Find the size of angle b

angles 2

Angles on a straight line add to 180°
b + 90° + 65° = 180°
b + 155° = 180°
b = 25°

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Angles around a point add to 360°

Example 3: Find the size of angle e

angles 19

Angles around a point add to 360°
e + 295° = 360°
e = 65°

Example 4: Find the size of angle f

angles 20

Angles around a point add to 360°
f + 131° + 108° + 52° = 360°
f + 291° = 360°
f = 69°

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Angles in a triangle add to 180°

Example 5: Find the size of angle j

angles 33

Angles in a triangle add to 180°
j + 71° + 53° = 180°
j + 124° = 180°
j = 56°

Example 6: Find the size of angle k

angles 34

Here we have an isosceles triangle. In an isosceles triangle two angles (and two sides) are equal.
There are lines on two of the sides to show that they are equal. The other side of an isosceles triangle is called the base.
The angles at the base of an isosceles triangle are equal. This means we have two 58° angles.

k + 58° + 58° = 180°
k + 116° = 180°
k = 64°

Example 7: Find the size of angle m

angles 35

We have another isosceles triangle. This time the missing angle is at the base.

m + m + 32° = 180°
2m = 148°
m = 74°

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Lesson

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Four labelled angles P, Q, R and S showing right, reflex, obtuse and acute examples with degree measures and a marked vertex

An angle measures the amount of turn between two straight lines that meet. The meeting point is called the vertex, and angles are measured in degrees, written ∘^\circ∘.

A right angle is 90∘90^\circ90∘, a straight line angle is 180∘180^\circ180∘, and a full turn is 360∘360^\circ360∘. These benchmark angles help you estimate and classify other angles quickly.

Acute angles are less than 90∘90^\circ90∘, obtuse angles are more than 90∘90^\circ90∘ but less than 180∘180^\circ180∘, and reflex angles are more than 180∘180^\circ180∘ but less than 360∘360^\circ360∘. Use the number or angle fact given, not just what the picture seems to show.

Questions

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29 exam-style questions

Practice questions

Question 1

3 marks

Here are four angles A, B, C and D.

Flashcards

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20 flashcards

Practice flashcards

An angle is measured in [     ]; the point where its arms meet is the [     ].

Angles Revision Guide

  1. GCSE
  2. /Maths
  3. /Angles

Revision notes for Edexcel GCSE Maths Angles. Open the guide for explanations and worked examples. Written against the Edexcel GCSE Maths (1MA1) specification, so the content matches what's examinable rather than general Maths background.

Revision guides

Practise questions

1 of 3

Two angles are on a straight line. One angle is 118∘118^\circ118∘. What is the size of the other angle?

Practise questions

1 of 3

Two angles are on a straight line. One angle is 75∘75^\circ75∘. What is the size of the other angle?

Practise questions

1 of 3

Four angles meet at a point. Three of them are 85∘85^\circ85∘, 110∘110^\circ110∘ and 95∘95^\circ95∘. Find the fourth angle.

Practise questions

1 of 3

Two angles, x and 65∘65^\circ65∘, lie on a straight line. Find the value of x.

Practise questions

1 of 3

A triangle has angles of 47∘47^\circ47∘ and 68∘68^\circ68∘. Find the third angle.

Practise questions

1 of 3

Two angles are on a straight line. If one angle measures 75∘75^\circ75∘, what is the size of the other angle?