Chapter 2, Problem 13RP

To determine

To Calculate: Measure of the complement.

Answer to Problem 13RP

The required measure is ${22.5}^{\circ }$

Explanation of Solution

Given information: In this question, it is given that measure of the supplement angle is five times the measure of complement angle.

Formula used: Sum of complementary angles is ${90}^{\circ }$ and the sum of supplementary angles is ${180}^{\circ }$

Calculation: Let both the angle be x

  $\left({180}^{\circ }-x\right)$ is the supplement

  $\left({90}^{\circ }-x\right)$ is the complement

Now, According to question:

  $\left({180}^{\circ }-x\right)$ = $\left(5\right)$

  $\left({90}^{\circ }-x\right)$

  →${180}^{\circ }-x=450-5x$

  →$4x=270$

  →$x=67.5$

Now, complement → ${90}^{\circ }-67.5=22.5$

Hence, the required measure is ${22.5}^{\circ }$