Geometry

Question Analysis

This question involves geometric knowledge of vertical angles and angle composition, as well as algebraic equation - solving.

 

Key Concept Explanation

Vertical angles: When two lines intersect, vertical angles are non - adjacent and opposite each other, and they have equal measures. Here, and are vertical angles, so .

Angle composition: An angle () can be divided into smaller adjacent angles ( and ), and the measure of the whole angle is the sum of the measures of its component angles.

Algebraic operations: We use the properties of equality to solve the linear equation for .

 

Step - by - Step Solution

1. First, combine like terms in the equation .

Combine the terms: