Chapter 12.3, Problem 24E

To determine

To find :the value of x and y.

Answer to Problem 24E

The value of x is ${91}^{\circ }$ andvalue of y is ${89}^{\circ }$ .

Explanation of Solution

Given : consider, the polygon provided in the question,

Formula used: the measure of sum interior angle of a regular n -gon is $\left(n-2\right)·{180}^{\circ }$ .

The sum of interior angle and its corresponding exterior angle = ${180}^{\circ }$

Calculation: to find the value of x , add all the interior angles and subtract from their sum,

  $\begin{array}{l}{90}^{\circ }+{90}^{\circ }+{128}^{\circ }+{141}^{\circ }+x^{\circ }=\left(5-2\right)·{180}^{\circ }\text{ [substitute the angles and n by 5]}\\ {449}^{\circ }+x^{\circ }=\left(3\right)·{180}^{\circ }\text{ [add, subtract]}\\ x^{\circ }={540}^{\circ }-{449}^{\circ }\text{ [subtract]}\\ x^{\circ }={91}^{\circ }\end{array}$

To find the value of y , subtract x value from the sum of interior and exterior angle,

  $\begin{array}{l}{91}^{\circ }+y^{\circ }={180}^{\circ }\text{ [substitute]}\\ y^{\circ }={180}^{\circ }-{91}^{\circ }\text{ [subtract]}\\ y^{\circ }={89}^{\circ }\end{array}$

Hence,The value of x is ${91}^{\circ }$ andvalue of y is ${89}^{\circ }$ .