# The ratio of the measures of two supplementary angles is 2:7. How do you find the measures of the angles?

Mar 29, 2017

${40}^{\circ} \text{ and } {140}^{\circ}$

#### Explanation:

color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(" the sum of 2 supplementary angles" = 180^@)color(white)(2/2)|)))

$\text{sum the parts of the ratio}$

$\Rightarrow 2 + 7 = 9 \text{ parts in total}$

Find the value of 1 part by dividing ${180}^{\circ} \text{ by } 9$

$\Rightarrow {180}^{\circ} / 9 = {20}^{\circ} \leftarrow \textcolor{red}{\text{ value of 1 part}}$

$\Rightarrow \text{2 parts } = 2 \times {20}^{\circ} = {40}^{\circ}$

$\Rightarrow \text{7 parts } = 7 \times {20}^{\circ} = {140}^{\circ}$

$\text{Thus the supplementary angles are " 40^@" and } {140}^{\circ}$