Geometry

Question Analysis

This question combines geometric concepts of vertical angles and angle - measure relationships on a straight - line with algebraic equation - solving.

 

Key Concept Explanation

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

Algebraic equations: We use the properties of equality to solve for the variable  in the equation formed from the angle relationship.

Angle on a straight - line: The sum of angles on a straight - line is , and  is related to  by the formula .

 

Step - by - Step Solution

1. Solve for :

Simplify the left - hand side of the equation . Combine  and  to get , so the equation becomes .

Move the  terms to one side. Subtract  from both sides: , resulting in .

Add  to both sides to isolate the term with :

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