Chapter 2, Problem 28RP

To determine

To find values of x and y.

Answer to Problem 28RP

  $Thevalueofxis25.74°andyis51.42°.$

Explanation of Solution

Given information:

  $\begin{array}{l}Sumofangles2x,2yandxform180°.\hfill \\ Sumofangles2y,xandyform180°.\hfill \end{array}$

Formula used:

The below property is used:

  $Anglesonstraightlineformasumequalto180°.$

Calculation:

From the below figure, we get

  $2x+2y+x=180°$

  $3x+2y=180° ----Equation1$

  $2y+x+y=180°$

  $x+3y=180° ----Equation2$

  

Multiplying Equation 2 by 3 on both sides, we get

  $3x+9y=540° ----Equation3$

Subtracting Equation 1 from Equation 3 on both sides, we get

  $7y=360°$

  $y=51.42°$

Substituting value of y in Equation 2, we get

  $x+\left(3*51.42°\right)=180°$

  $x=180°-154.26°$

  $x=25.74°$