Chapter 1.5, Problem 24PSC

To determine

To Calculate: The measure of each angle.

Answer to Problem 24PSC

  $\begin{array}{l}\text{Larger angle }=\left(37.5\right)°\\ \text{Smaller angle}=\left(22.5\right)°\end{array}$

Explanation of Solution

Given:

Measure of two angles are in the ratio 5 : 3.

  $\text{Larger angle =}30°\text{ +}\frac{1}{2}\left(\text{Larger angle}-\text{Smaller angle}\right)$

Concept Used:

Bisectors divides the angle into two equal parts.

Calculation:

Since, the measure of two angles are in the ratio 5 : 3.

  $\begin{array}{l}\Rightarrow \text{Required angles are 5}x\text{and }3x\\ \text{Larger angle }=5x\\ \text{Smaller angle}=3x\\ \because \text{Larger angle =}30°\text{ +}\frac{1}{2}\left(\text{Larger angle}-\text{Smaller angle}\right)\\ \Rightarrow \left(5x\right)°=30°+\frac{1}{2}\left(\text{5}x-3x\right)°\\ \Rightarrow \left(5x\right)°=30°+\left(x\right)°\\ \Rightarrow \left(4x\right)°=30°\\ \Rightarrow x=\left(7\frac{1}{2}\right)°=\left(7.5\right)°\\ \Rightarrow \text{Larger angle }=\left(5\times 7.5\right)°=\left(37.5\right)°\\ \text{Smaller angle}=\left(3\times 7.5\right)°=\left(22.5\right)°\end{array}$

Conclusion:

  $\begin{array}{l}\text{Larger angle }=\left(37.5\right)°\\ \text{Smaller angle}=\left(22.5\right)°\end{array}$