Chapter 11.1, Problem 8CYU

To determine

To find the measure of given angles.

Answer to Problem 8CYU

$x={20.4}^{\circ }$ & $\angle Q={139.2}^{\circ },\angle R={40.8}^{\circ }$

Explanation of Solution

Given:

$\angle Q$ & $\angle R$ are supplementary, $\angle Q={\left(6x+16.8\right)}^{\circ }$ and $\angle R=2x^{\circ }$ .

Concept used:

Two angles are supplementary if their sum is ${180}^{\circ }$ .

Calculation:

Since $\angle Q$ & $\angle R$ are supplementary, therefore

  $\begin{array}{l}\angle Q+\angle R={180}^{\circ }\\ \Rightarrow {\left(6x+16.8\right)}^{\circ }+2x^{\circ }={180}^{\circ }\\ \Rightarrow 8x+{16.8}^{\circ }={180}^{\circ }\\ \Rightarrow 8x={180}^{\circ }-{16.8}^{\circ }\\ \Rightarrow 8x={163.2}^{\circ }\\ \Rightarrow x={20.4}^{\circ }\end{array}$

Hence,

  $\begin{array}{l}\angle Q={\left(6x+16.8\right)}^{\circ }={\left(6\times 20.4+16.8\right)}^{\circ }={139.2}^{\circ }\\ \angle R=2x^{\circ }=2\times {20.4}^{\circ }={40.8}^{\circ }\end{array}$