Geometry

Question Analysis

This question integrates geometric angle - relationship knowledge and algebraic equation - solving.

 

Key Concept Explanation

Vertical angles: When rays intersect at a point, vertical angles are non - adjacent and opposite, and they have equal measures. Here,  and  are vertical angles.

Angle composition: An angle can be composed of smaller adjacent angles. In this case,  is composed of  and .

Algebraic operations: We use the properties of equality (such as adding, subtracting, multiplying, or dividing both sides of an equation by the same non - zero number) to isolate the variable .

 

Step - by - Step Solution

1. Simplify the left - hand side of the equation :

Combine the constant terms  and . Since , the equation becomes .

 

2. Move the  terms to one side:

Subtract  from both sides of the equation:

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