Chapter 12.1, Problem 28E

To determine

To find: The value of $x$ .

Answer to Problem 28E

The value of $x$ is ${15}^{\circ }$

Explanation of Solution

Given: Linear pair of angles

  $5x^{\circ },7x^{\circ }$ .

Calculation:

Since, sum of the angles forming a linear pair is ${180}^{\circ }$ .

Therefore,

  $5x^{\circ }+7x^{\circ }={180}^{\circ }$........(1)

Find $x$ using equation (1)

  $5x^{\circ }+7x^{\circ }={180}^{\circ }$

  $\begin{array}{l}\Rightarrow 12x^{\circ }={180}^{\circ }\\ \Rightarrow x=\frac{{180}^{\circ }}{{12}^{\circ }}\\ \Rightarrow x={15}^{\circ }\end{array}$

Thus, the value of $x$ is ${15}^{\circ }$ .

Therefore, the unknown angle measures are ${75}^{\circ }$ , ${105}^{\circ }$ .