Geometry

Question Analysis

This question combines geometric concepts of vertical angles and right - angled angles 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. So, the measure of is equal to the measure of .

Right - angled angles: A right - angle has a measure of . In this case, as indicated by the right - angle symbol in the diagram.

Algebraic equations: We use the rules of equality to perform operations on both sides of the equation formed from the angle relationships to isolate and find the value of .

 

Step - by - Step Solution

1. Given the equation .

First, combine like terms on the left - hand side. Combine the terms: