A polygon has n sides. An interior angle of the polygon and an adjacent exterior angle form a straight angle. What is the measure of each interior angle of the polygon?
no way to tell. For any polygon, the interior and exterior angles form a straight line.
To solve this problem, we need to understand the relationship between the interior and exterior angles of a polygon.
First, let's consider a regular polygon, where all sides and angles are equal. In a regular polygon with n sides, each interior angle measures (n-2)/n * 180 degrees.
Now, let's apply this knowledge to solve the problem at hand. We are given that an interior angle and an adjacent exterior angle form a straight angle, which measures 180 degrees.
Let's assume the measure of the interior angle is x degrees. The adjacent exterior angle, which forms a straight angle, will be 180 - x degrees.
According to the relationship between the interior and exterior angles of a polygon, the exterior angle is always supplementary to the interior angle. In other words, the sum of the interior and exterior angles is 180 degrees.
So, we can set up the following equation:
x + (180 - x) = 180
By simplifying the equation, we get:
180 - x + x = 180
This simplifies to:
180 = 180
Since this equation is true for any value of x, we can conclude that the measure of each interior angle of the polygon is x degrees.
Therefore, the measure of each interior angle of the polygon is x degrees, where x can be any value.