In triangle ABC, the exterior angle at C is $110^\circ$ and the interior angle at A is $45^\circ$. What is the measure of angle B?

Explanation

1. 01

   The exterior angle of a triangle equals the sum of the two interior angles not adjacent to it.

2. 02

   The exterior angle at C is therefore $A + B$, so $110^\circ = 45^\circ + B$.

3. 03

   This gives $B = 65^\circ$.

4. 04

   Check by the longer route: the interior angle at C is $180^\circ - 110^\circ = 70^\circ$, and $45^\circ + 65^\circ + 70^\circ = 180^\circ$.