Question

19. Two angles are supplementary. The measure of one angle is four times the measure of the other angle. Find the measure of each angle.

Answer 1

36 and 144

Explanation

Two Angles are Supplementary when they add up to 180 degrees

Step 1

Let

x= angle 1

y= angle2

The measure of one angle is four times the measure of the other angle,then

$\begin{gathered} \text{angle}1=4\cdot\text{angle}2\text{ } \\ x=4y\text{ Equation(1)} \end{gathered}$

x and y are supplementary angles , then

$x+y=180\text{ Equation (2)}$

Step 2

use Equation (1) and (2) to find x and y

$\begin{gathered} x=4y \\ x+y=180 \end{gathered}$

replace Equation (1) in Equation (2)

$\begin{gathered} 4y+y=180 \\ 5y=180 \\ y=\frac{180}{5} \\ y=36 \end{gathered}$

replace the value of y= 36 in equation (1) to find x

$\begin{gathered} x=4y \\ x=4\cdot36 \\ x=144 \end{gathered}$

Hence, the answer is 36 and 144