Chapter 6.1, Problem 54STP

To determine

The measure of angle ABC.

Answer to Problem 54STP

Option A. 140 is correct.

Explanation of Solution

Given:

The given figure is:

Calculation:

The sum of the measures of interior angles of an n-sided polygon is:

  $\left(n-2\right)180$

The given figure is of a regular nonagon, having 9 sides.

So, put the value in the formula:

  $\begin{array}{l}Sum=\left(n-2\right)180\\ Sum=\left(9-2\right)180\\ Sum=\left(7\right)180\\ Sum=1260\end{array}$

As the object is a regular 9-gon, all interior angles are congruent.

Calculating the measure of one interior angle:

  $\begin{array}{l}\frac{\text{Sum of interior angle measures}}{\text{Number of congruent angles}}=\frac{1260}{9}\\ \text{ =140}\end{array}$

Hence, Option A. 140 is correct.