Chapter 12, Problem 11CT

To determine

To find: The unknown angle.

Answer to Problem 11CT

The unknown angles $\angle \text{p}$ is ${129}^{\circ }$ .

Explanation of Solution

Given information:

  

Calculation: From the figure it is clear that $\angle {51}^{\circ }$ is an interior angle and $\angle {\text{p}}^{\circ }$ is an exterior angle of the given triangle.

The sum of an exterior angle and its adjacent interior angle is ${180}^{\circ }$ .

Therefore, $\angle {\text{p}}^{\circ }$ $+$ ${51}^{\circ }$ $=$ ${180}^{\circ }$$\mathrm{......}(1)$

Let’s find the value of $\angle {\text{p}}^{\circ }$ ,

  $\begin{array}{c}\angle {\text{p + 51}}^{\circ }={180}^{\circ }\\ \angle \text{p}={180}^{\circ }-{51}^{\circ }\\ \angle \text{p}={129}^{\circ }\end{array}$

Hence, The unknown angles $\angle \text{p}$ is ${129}^{\circ }$ .