Chapter 12.3, Problem 26E

To determine

To find :the value of x and y.

Answer to Problem 26E

The value of x is ${20}^{\circ }$ andvalue of y is ${120}^{\circ }$ .

Explanation of Solution

Given : 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 divide,

  $\begin{array}{l}3x^{\circ }+4x^{\circ }+2x^{\circ }=\left(3-2\right)·{180}^{\circ }\text{ [substitute n by 3 and angles]}\\ 9x^{\circ }=\left(1\right)·{180}^{\circ }\text{ [add and subtract]}\\ 9x^{\circ }={180}^{\circ }\\ x^{\circ }={90}^{\circ }\text{ [divide]}\end{array}$

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

  $\begin{array}{l}3x^{\circ }+y^{\circ }={180}^{\circ }\\ 3·{20}^{\circ }+y^{\circ }={180}^{\circ }\text{ [substitute]}\\ y^{\circ }={180}^{\circ }-{60}^{\circ }\text{ [subtract]}\\ y^{\circ }={120}^{\circ }\end{array}$

Hence,The value of x is ${20}^{\circ }$ andvalue of y is ${120}^{\circ }$ .