Chapter 6.1, Problem 55STP

a

To determine

The measure of angle y.

Answer to Problem 55STP

  $m\angle y=72$

Explanation of Solution

Given:

The given figure is:

Line l passes through AE.

Calculation:

Angle y is the exterior angle of the given polygon ABCDE.

The sum of the measures of exterior angles of convex polygon, one angle at every vertex is 360.

Given figure is a pentagon with 5 congruent interior angles. The exterior angles of the pentagon are also congruent because angles supplementary to congruent angles are also congruent.

Suppose, the measure of each exterior angle is n.

Then,

  $\begin{array}{l}5n=360\\ n=\frac{360}{5}\\ n=72\\ \therefore m\angle y=72\end{array}$