Question

use the appropriate theorem(s) to find the measure of ∠1.

Explanation:

Answer:

To find the measure of \( \angle 1 \) using the appropriate theorem (likely the Vertical Angles Theorem or Linear Pair Theorem), if the given angle is \( 58^\circ \) and \( \angle 1 \) is supplementary to it (forming a linear pair), then \( \angle 1 = 180^\circ - 58^\circ = 122^\circ \). If they are vertical angles, \( \angle 1 = 58^\circ \). Assuming a linear pair (since the diagram shows intersecting lines with adjacent angles), the measure of \( \angle 1 \) is \( \boxed{122^\circ} \) (or \( \boxed{58^\circ} \) if vertical angles; more context from the diagram suggests linear pair here).

(Note: Based on typical intersecting lines problems, if one angle is \( 58^\circ \) and \( \angle 1 \) is adjacent forming a linear pair, the answer is \( 122^\circ \).)