Find the measure of one interior angle for the following regular polygon

Step-by-step explanation:

I am assuming that by "interior" angle you do not mean the central angle.

This is a 10-sided polygon, a decagon. That means that there are 10 triangles that can extend from the center, with their sides being equal to the radii of the decagon. If we extract one of these triangles we can find what the interior angle is. The vertex angle measures 360/10 which is 36.

Split this triangle in half from the vertex to the base, creating a right triangle. The vertex angle is also split in half, making this angle (the vertex angle is the one at the top of the triangle) 18 degrees. We already know that one angle inside this right triangle is 90 (definition of a right triangle) and to find the other one, we apply the Triangle Angle-Sum Theorem:

180 - 18 - 90 = 72 degrees. That is the measure of the base angle that is NOT the right angle, obviously.

x = 45

135°

Step-by-step explanation:

180 - 45 = 135

3x = 135

3x/3 = 135/3

x = 45