Chapter 2, Problem 31RP

To determine

To find by how much value x exceed y.

Answer to Problem 31RP

The value “ x ” exceeds “ y ” by $110°$

Explanation of Solution

Given information:

  $\begin{array}{l}Sumofangles\left(x+2y\right)°and\left(x–2y\right)°form180°.\hfill \\ Sumofangles\left(x–2y\right)°and50°form180°.\hfill \end{array}$

Formula used:

The below property is used:

  $Anglesonstraightlineformasumequalto180°.$

Calculation:

From the below figure, we get

  $x+2y+x-2y=180° ----Equation1$

  $x–2y+50°=180° ----Equation2$

  

From Equation 1, we get

  $2x=180°$

  $\therefore x=90°$

From Equation 2, we get

  $90°-2y+50°=180°$

  $\therefore 140°-2y=180°$

  $\therefore -2y=40°$

  $\therefore y=-20°$

  $\therefore xexceedsyby\left|90°-\left(-20°\right)\right|=110°$