Question

in the diagram, the measure of ∠1 is 55°. if line y is rotated 5° clockwise about the point of intersection, what is the new measure of ∠3?
diagram of two intersecting lines x and y, forming angles 1, 2, 3, 4
options: 60°, 130°, 50°, 120°

Explanation:

Step1: Find original ∠3 measure

Original $\angle 1 = 55^\circ$, and vertical angles are equal, so original $\angle 3 = 55^\circ$.

Step2: Adjust for rotation effect

Rotating line $y$ 5° clockwise decreases $\angle 1$ by 5°, so new $\angle 1 = 55^\circ - 5^\circ = 50^\circ$.

Step3: Find new ∠3 measure

Vertical angles remain equal after rotation, so new $\angle 3 =$ new $\angle 1 = 50^\circ$.

Answer:

$50^\circ$