Chapter 12, Problem 10PSQ

To determine

To find: The value of $x\text{ or }y$ .

Answer to Problem 10PSQ

The value of $y$ is ${65}^{\circ }$ .

Explanation of Solution

Given information:

  

Calculation: The given figure represents a quadrilateral with $4$ unequal sides.

Sum of the interior angles of a quadrilateral is ${360}^{\circ }$ .

Therefore, ${101}^{\circ }+y^{\circ }+{(2y+10)}^{\circ }+{(y-11)}^{\circ }={360}^{\circ }$$\mathrm{......}(1)$

Let’s find the value of $y$ from equation $(1)$ ,

  $\begin{array}{c}{101}^{\circ }+y+{(}^2+{(}^y={360}^{\circ }\\ {101}^{\circ }+y+2y+{10}^{\circ }+y-{11}^{\circ }={360}^{\circ }\\ 4y={360}^{\circ }-{100}^{\circ }\\ 4y={260}^{\circ }\\ y=\frac{{260}^{\circ }}{4}\\ y={65}^{\circ }\end{array}$

Hence, The value of $y$ is ${65}^{\circ }$ .