Question

∠1 and ∠2 are supplementary angles, and ∠1 and ∠3 are vertical angles. if the measure of ∠3 = 60°, what is the measure of ∠2? select one answer a 30° b 60° c 90° d 120°

Explanation:

Step1: Recall vertical angles property

Vertical angles are equal, so \( \angle 1=\angle 3 \). Given \( \angle 3 = 60^\circ \), then \( \angle 1=60^\circ \).

Step2: Recall supplementary angles property

Supplementary angles sum to \( 180^\circ \), so \( \angle 1+\angle 2 = 180^\circ \). Substitute \( \angle 1 = 60^\circ \): \( 60^\circ+\angle 2=180^\circ \). Solve for \( \angle 2 \): \( \angle 2=180^\circ - 60^\circ=120^\circ \).

Answer:

D \( 120^\circ \)