Chapter 2.2, Problem 23PSB

To determine

To calculate: to find two fifth of measure of complement.

Answer to Problem 23PSB

  ${12}^{\circ }$

Explanation of Solution

Given information: supplement of an angle is ${30}^{\circ }$ less than five times the measure of its complement.

Formula Used: sum of two supplementary angle is ${180}^{\circ }$ and sum of two complementary angle is ${90}^{\circ }$ .

Calculation: let measure of the angle is $x^{\circ }$

According to given condition,

  $\begin{array}{l}$ 5{(90-x)}^{\circ }-{(180-x)}^{\circ }={30}^{\circ }$\therefore {450}^{\circ }-5x^{\circ }-180+x^{\circ }={30}^{\circ }\\ \therefore 4x^{\circ }={240}^{\circ }\\ \therefore x={60}^{\circ }\end{array}$

  $\therefore$ Two fifth of its compliment =

  $\begin{array}{l}=\frac{2}{5}\times ({90}^{\circ }-{60}^{\circ })\\ =\frac{2}{5}\times {30}^{\circ }\\ ={12}^{\circ }\end{array}$