Question

in the diagram, the measure of ∠1 is 55°. if line y is rotated 5° clockwise about point of intersection, what is the new measure of ∠3?

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. Initially, $\angle1$ and $\angle3$ are vertical angles, so $\angle3 = \angle1=55^{\circ}$.

Step2: Consider the rotation effect

When line $y$ is rotated $5^{\circ}$ clock - wise about the point of intersection, the measure of $\angle3$ will decrease by $5^{\circ}$.
$55^{\circ}- 5^{\circ}=50^{\circ}$

Answer:

$50^{\circ}$