Geometry

Question Analysis:

This question involves calculating the measure of an angle () using the properties of adjacent angles and right - angles.

 

Key Concept Explanation:

A right - angle measures . When two adjacent angles form a right - angle, the sum of their measures is . If the measure of one of the adjacent angles is known, we can find the measure of the other by subtraction.

 

Step - by - Step Solution:

1. Identify the relevant angles:

In the figure, and are adjacent angles, and together they form a right - angle at vertex . We know that , and a right - angle has a measure of .

 

2. Apply the angle relationship:

Since

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