Skill: Find unknown angle measures

An unknown angle is often a missing part of a larger angle.

First, identify:

• the whole angle
• the known part
• the unknown part

Then use:

$$\text{unknown part}=\text{whole angle}-\text{known part}$$

Remember that turning an angle in a different direction does not change its measure.

Example

Angle $(ABC)$ is a right angle, so its total measure is $(90^\circ)$. Ray $(BD)$ splits it into two angles. One angle measures $(35^\circ)$. Find $(m\angle DBC)$.

You can picture it like this:

A
 \ 
  \ 35°
   B────────C

1. The whole angle is a right angle:

$$m\angle ABC=90^\circ$$

2. The known part is:

$$35^\circ$$

3. The two smaller angles make the whole angle:

$$35^\circ+m\angle DBC=90^\circ$$

4. Subtract the known part from the whole:

$$m\angle DBC=90^\circ-35^\circ$$

5. Calculate:

$$m\angle DBC=55^\circ$$

So, the unknown angle measures $(55^\circ)$.

Check: $(35^\circ+55^\circ=90^\circ)$, which is the measure of a right angle.