Geometry

Question Analysis

The main focus of this question is to find the unknown interior angle of a polygon. It requires applying the concept of the sum of interior angles of a polygon, which is a fundamental characteristic whether the polygon is regular or irregular.

 

Key Concept Explanation

The sum of the interior angle measures of a polygon is given by the formula , where is the number of sides of the polygon. This formula is derived from dividing the polygon into triangles, with each triangle having an interior angle sum of .

 

Step - by - Step Solution

1. Determine the number of sides:

The given polygon is a quadrilateral, so .

2. Calculate the sum of interior angles:

Substitute into the formula .

First, calculate : .

Then, find : .

3. Set up an equation to find :

The sum of the known interior angles is .

Since the sum of all interior angles is , we have the equation

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