Chapter 12, Problem 9PSQ

To determine

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

Answer to Problem 9PSQ

The value of $x$ is ${41}^{\circ }$ .

Explanation of Solution

Given information:

  

Calculation: Provided figure represents a triangle.

Therefore, The sum of the interior angles of a triangle is ${180}^{\circ }$ .

Hence, from the figure it is clear that,

  ${(2x+4)}^{\circ }+{(x+12)}^{\circ }+x^{\circ }={180}^{\circ }\mathrm{......}(1)$

Let’s solve the equation $(1)$ ,

  $\begin{array}{c}$ {(2x+4)}^{\circ }+{(x+12)}^{\circ }+x^{\circ }={180}^{\circ }$2x+4+x+12+x=180\\ 4x+16=180\\ 4x=180-16\\ x=\frac{164}{4}\\ x={41}^{\circ }\end{array}$

Hence, The value of $x$ is ${41}^{\circ }$ .