Chapter 2.8, Problem 12PSB

To determine

To find the measures of angles $\angle 4,\angle 5$ and $\angle 6$

Answer to Problem 12PSB

  $\begin{array}{l}\angle 1\text{ will be }36°\\ \angle 2\text{ will be }90°\\ \text{and }\angle 3\text{ will be 54}°\end{array}$

Explanation of Solution

Given information :

Measures of angles are in the ratio $2:5:3$

Formula used:

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

Calculation:

Let measures of $\angle 4,\angle 5\text{ and }\angle 6$ be $\angle 2\text{x}°,\angle 5\text{x}°\text{ and }\angle 3\text{x}°$

Since, sum of $\angle 4,\angle 5\text{ and }\angle 6$ formed on same side of the straight line is equal to $180°$ , we have

  $\begin{array}{l}\angle 4+\angle 5+\angle 6=180\\ \Rightarrow 2\text{x}°+5\text{x}°+3\text{x}°=180°\\ \Rightarrow 10x°=180°\\ \Rightarrow x=18°\end{array}$

Hence,

  $\begin{array}{l}\angle 1=2x°=2\times 18°=36°\\ \angle 2=5x°=5\times 18°=90°\end{array}$

And $\angle 3=3x°=3\times 18°=54°$