Question

proving angles congruent type your answer and then click or tap done x=135 diagram of two intersecting lines with angle labels, and some chinese text

Explanation:

Step1: Identify vertical angles

When two lines intersect, vertical angles are equal. Here, the given angle and the angle we need to find (let's say \( x \)) are vertical angles? Wait, no, maybe supplementary? Wait, the diagram shows two intersecting lines, forming vertical angles. Wait, the given angle is \( 115^\circ \)? Wait, maybe the angle adjacent to it is supplementary. Wait, no, vertical angles are equal. Wait, maybe the problem is about vertical angles or linear pairs. Wait, if two lines intersect, vertical angles are congruent, and linear pairs are supplementary (sum to \( 180^\circ \)).

Wait, let's assume the given angle is \( 115^\circ \), and we need to find the measure of the vertical angle or the adjacent angle. Wait, the problem says "Finding Angles Congruent" and "x = 115" maybe? Wait, the diagram has two intersecting lines, so vertical angles are congruent. So if one angle is \( 115^\circ \), its vertical angle is also \( 115^\circ \), and the adjacent angles are \( 180 - 115 = 65^\circ \), but since the problem is about congruent angles (vertical angles are congruent), so the congruent angle to \( 115^\circ \) is also \( 115^\circ \).

Step2: Apply vertical angles theorem

Vertical angles theorem states that vertical angles are congruent (equal in measure). So if one angle formed by intersecting lines is \( 115^\circ \), its vertical angle is also \( 115^\circ \).

Answer:

\( 115^\circ \) (assuming the angle is a vertical angle to the given \( 115^\circ \) angle, so by vertical angles theorem, they are congruent)