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Calculating angles around a point

What is a full turn?

  • A full turn around a point is 360°. Angles around a point always sum to 360°.
  • Knowing one of the angles allows you to calculate the other angles around the point, often without needing a protractor.

Examples


Example 1: This diagram shows that there are two angles to be found.
What are angles C and D?

ExamplesThe angles either side of the straight line must add up to 180°.
To f​ind angle C, you can subtract 112° from 180°.
180° ​- 112° = 68°
ExamplesAngle C is 68°.
To find angle D, subtract 145° from 180°.
180° - ​145° = 35°
ExamplesAngle D is 35°.
Example 2: What is the value of A?
ExamplesThese two angles are around a point. They must add up to 360°.
13​5° + A = 360°
We can rearrange this to find angle A:
A = 360° - 135°
Therefore:
360° - 135° = 225°
Angle A is 225°.
ExamplesHowever, sometimes you need to find more than one angle around a point.
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