Maths: angles in diagrams

Watch it happen

Angles on a straight line

Two angles sit on a straight line. One is 70°. The other is marked x. Estimate first: is x wider or narrower than a right angle?

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The idea

Angles are measured in degrees (°). The facts that solve most problems: angles on a straight line add to 180°; angles around a point add to 360°; a right angle is 90°, so angles in a corner or square corner split 90° between them; and the angles inside a triangle add to 180°.

To find a missing angle, decide which fact fits the picture, add up the angles you know, and subtract from the total (180°, 360° or 90°).

Estimate first: an angle smaller than a right angle (acute) must be under 90°, and one bigger (obtuse) between 90° and 180°. If your answer breaks that, recheck.

Worked example

The diagram shows angles on a straight line: 102° and an angle marked x. Work out the size of the angle marked x. Give your answer in degrees.

1. Angles on a straight line always add up to 180° — that is the anchor fact. The picture shows the fan of angles sitting on one straight line.

   

2. Add up the angles you can see: 102 = 102°.

   

3. The unknown angle makes the total up to 180°, so x = 180 − 102 = 78°.

   

4. Sense-check: 102 + 78 = 180 ✓, and 78° looks the right size next to its neighbours in the picture.

   

Answer: x = 78° — angles on a straight line add up to 180°, so x = 180 − 102 = 78°.

Try one yourself

The diagram shows a right angle split into two parts. One part is 61°. Work out the size of the angle marked x. Give your answer in degrees.

Watch out

• Using 180° for angles around a point (that total is 360°).
• Subtracting from the wrong total — name the fact you are using before you calculate.
• Giving an answer over 180° for an angle that is clearly acute in the diagram.