Chapter 1, Problem 8RP

To determine

The find the measures of angles $\angle 1,\angle 2$ and $\angle 3$

Answer to Problem 8RP

  $\begin{array}{l}\angle 1\text{ will be }30°\\ \angle 2\text{ will be }90°\\ \text{and }\angle 3\text{ will be 6}0°\end{array}$

Explanation of Solution

Given information:

Measures of angles are in the ratio $1:3:2$

Formula used:

Sum of the angles formed on the same side of the straight line is equal to $180°$

Calculation:

Let measures of $\angle 1,\angle 2\text{ and }\angle 3$ be $\angle \text{x}°,\angle 3\text{x}°\text{ and }\angle 2\text{x}°$

Since, sum of $\angle 1,\angle 2\text{ and }\angle 3$ formed on same side of the straight line is equal to $180°$ , we have

  $\begin{array}{l}\angle 1+\angle 2+\angle 3=180\\ \Rightarrow \text{x}°+3\text{x}°+2\text{x}°=180°\\ \Rightarrow 6x°=180°\\ \Rightarrow x=30°\end{array}$

Hence,

  $\begin{array}{l}\angle 1=x°=30°\\ \angle 2=3x°=3\times 30°=90°\end{array}$

And

  $\angle 3=2x°=2\times 30°=60°$