Angles Around a Point

Angles Around a Point

Angles around a point add up to 360°. If all the angles meet at the same point, you can use this total to find a missing angle by subtraction or by solving a simple equation.

Method

1. List the known angles. Write down every angle value given in the diagram.
2. Add the known angles. If some angles are expressions, combine like terms first.
3. Use 360° as the total.
   • If one angle is missing: missing angle = 360° - sum of known angles
   • If two or more angles are unknown: set up an equation using the fact that the total is 360°.
4. Simplify your answer. Carry out any arithmetic carefully and reduce the result if needed.

Check your work

• Add your answer back to the other angles. The total should be 360°.
• Make sure your angle makes sense in the context of the diagram.

Example strategy

If the angles are split around a point into several parts, start by finding the total of the parts you already know. Then subtract that total from 360°. If an expression appears, solve it first and then use the value in the total.

This method works every time because all angles around one point make a full turn.