Geometry

Question Analysis

This question involves the angle - addition postulate. The main focus is using the relationship between the three given angles to determine the value of and then find the measures of and .

Key Concept Explanation

If a point lies in the interior of , then according to the angle - addition postulate.

Step - by - Step Solution

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

Substitute the given angle measures into . So, .

2. Simplify the left - hand side of the equation:

Combine like terms: . The equation becomes .

3. Solve for :

Add 6 to both sides of the equation: .

Divide both sides by 24: