Geometry

Question Analysis

This question involves the concepts of vertical angles and supplementary angles in geometry.

 

Key Concept Explanation

Vertical angles: When two lines intersect, vertical angles are non - adjacent angles opposite each other and are congruent.

Supplementary angles: Two angles are supplementary if the sum of their measures is .

 

Step - by - Step Solution

1. Find the value of :

Since the angles and are vertical angles, they are equal. So, we set up the equation .

Subtract from both sides: , which simplifies to .

Add 29 to both sides: , getting .

Divide both sides by 2:

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