Chapter 1.2, Problem 21PSC

To determine

To Find: $\text{The value of }x\text{and }y.$ .

Answer to Problem 21PSC

  $x=10°\text{and}y=20°$

Explanation of Solution

Given:

  $\begin{array}{l}\angle TRS\text{ is a straight angle}\text{.}\\ \angle TRX\text{ is a right angle}\text{.}\\ m\left(\angle TRS\right)=2x+5y\\ m\left(\angle XRS\right)=3x+3y\end{array}$

  

Concept Used:

Sum of linear pair of angles is $180°$

Calculation:

Here

  $\begin{array}{l}\angle TRS\text{ is a straight angle}\text{.}\\ \angle TRX\text{ is a right angle}\text{.}\\ m\left(\angle TRS\right)=2x+5y\\ m\left(\angle XRS\right)=3x+3y\end{array}$

  $\begin{array}{l}\Rightarrow \angle TRS=180°\\ \Rightarrow 2x+5y=180°\left(1\right)\\ \text{and }\angle TRX=90°\\ \Rightarrow 3x+3y=90°\left(2\right)\\ \text{Operate 3}\times \left(1\right)-2\times \left(2\right),\text{we get}\\ 9y=180°\\ \Rightarrow y=20°\left(3\right)\\ \text{Using}\left(3\right),\text{in }\left(2\right)\text{ get}\\ 3x+3\times 20°=90°\\ \Rightarrow 3x=90°-60°\\ \Rightarrow 3x=30°\\ \Rightarrow x=10°\\ \therefore x=10°\text{and}y=20°\end{array}$

Conclusion:

  $x=10°\text{and}y=20°$