Chapter 2.4, Problem 21PSC

To determine

To calculate: Ratio of angle to its complement.

Answer to Problem 21PSC

3:2

Explanation of Solution

Given information: Ratio of an angle to its supplement is 3:7.

Calculation: let measure of the angle be $x^{\circ }$ , then its supplement is ${(180-x)}^{\circ }$ and complement is $\begin{array}{l}\frac{x}{90-x}\\ =\frac{54}{90-54}\\ =\frac{54}{36}\\ =3:2\end{array}$ .

Now, given that $x^{\circ }:{(180-x)}^{\circ }\frac{3}{7}$

  $\begin{array}{l}\Rightarrow \frac{x}{180-x}=\frac{3}{7}\\ \Rightarrow 7x=540-3x\\ \Rightarrow 10x={540}^{\circ }\\ \therefore x={54}^{\circ }\end{array}$

Ratio of $x^{\circ }$ to its complement =

  $\begin{array}{l}\frac{x}{90-x}\\ =\frac{54}{90-54}\\ =\frac{54}{36}\\ =3:2\end{array}$