Geometry

Question Analysis

This question involves the angle - addition postulate. The main focus is on finding the value of and then using it to calculate the measures of the individual angles and given the measure of the larger angle .

Key Concept Explanation:

The angle - addition postulate states that if point lies in the interior of , then .

Step - by - Step Solution:

1. Set up the equation based on the angle - addition postulate:

Substitute the given angle expressions into . We have .

First, simplify the right - hand side by combining like terms: .

So the equation becomes .

Subtract 4 from both sides: , which gives