Geometry

Question Analysis

This question involves the angle - addition postulate. The main focus is using this postulate to find the value of and then determine the measures of and .

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:

Substitute the given angle measures into the angle - addition formula: .

2. Simplify the left - hand side:

Combine like terms: .

3. Solve for :

Subtract from both sides: .

Add 3 to both sides: .

Divide both sides by 11: .

4. Calculate the angle measures:

For

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