Chapter 12.1, Problem 27E

To determine

To find: The value of $x$ .

Answer to Problem 27E

The value of $x$ is $9^{\circ }$

Explanation of Solution

Given: Vertically opposite angles

  $6x^{\circ },{\left(2x+36\right)}^{\circ }$ .

Calculation:

Since, vertically opposite angles are equal.

Therefore,

  $6x^{\circ }={\left(2x+36\right)}^{\circ }$.........(1)

Find $x$ using equation (1)

  $6x^{\circ }={\left(2x+36\right)}^{\circ }$

  $\begin{array}{l}\Rightarrow 6x^{\circ }-2x^{\circ }={36}^{\circ }\\ \Rightarrow 4x^{\circ }={36}^{\circ }\\ \Rightarrow x=\frac{{36}^{\circ }}{4^{\circ }}\\ \Rightarrow x=9^{\circ }\end{array}$

Thus, the value of $x$ is $9^{\circ }$ .

Therefore, vertically opposite angles are ${54}^{\circ },{54}^{\circ }$ .