Question

if angle 1 and angle 2 are vertical angles, angle 2 and angle 3 are complementary angles, and the measure of angle 3 = 56, find the measure of angle 1

Answer 1

We know that

`m\angle3=56`

If angle 2 and angle 3 are complementary, then by its definition we can express the following.-

`\begin{gathered} m\angle2+m\angle3=90 \\ m\angle2=90-m\angle3 \\ m\angle2=90-56=34 \end{gathered}`

Then, angle 1 and angle 2 are equal by definition of vertical angles.

`m\angle1=m\angle2=34`

Therefore, angle 1 measures 34°.