Question

The measure of the seven angles in a nonagon measure 138, 154, 145, 132, 128, 147, and 130. If the two remaning angles are equal in measure, what is the measure of each angle

Answer 1

The measure of each angle is 143 degrees.

Explanation:

We are given the following in the question:

A nonagon in which measure of seven angles are:

138, 154, 145, 132, 128, 147, 130.

Angle sum property of a nonagon:

• The sum of interior angles if a nonagon are 1260 degrees.

Let the two equal angle of nonagon be x degrees. Thus, we can write:

`138+154+ 145+132+ 128+ 147+ 130+2x = 1260\\\Rightarrow 974 + 2x = 1260\\\Rightarrow 2x = 1260 - 974\\\Rightarrow 2x = 286\\\Rightarrow x = 143`

Thus, the measure of two equal angles is 143 degrees.