Question

find the measure of angle 1.

Explanation:

Step1: Identify vertical - angle relationship

Angle 1 and the angle adjacent to the 64 - degree angle are vertical angles.

Step2: Use linear - pair property

The 64 - degree angle and the angle adjacent to it form a linear pair. So the measure of the angle adjacent to the 64 - degree angle is $180^{\circ}-64^{\circ}=116^{\circ}$.

Step3: Determine angle 1

Since angle 1 and the angle adjacent to the 64 - degree angle are vertical angles, they are equal. So angle 1 is $116^{\circ}$.

Answer:

$116^{\circ}$