Geometry

Question Analysis

This question combines geometric concepts of vertical angles and angle composition with 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.

Angle composition: An angle () can be made up of smaller adjacent angles ( and ).

Algebraic equations: We use the properties of equality to perform operations on both sides of the equation to isolate the variable .

 

Step - by - Step Solution

1. Given the equation .

First, combine like terms on the left - hand side. Combine the  terms: , and combine the constant terms: . So the equation becomes

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