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The ratio of the measure of two supplementary angles is 14:4. Find the measure of each angle.

The ratio of the measure of two supplementary angles is $14$ : $4$ . Find the measure of each angle.

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Find missing angles in quadrilaterals II

Full solution

Q. The ratio of the measure of two supplementary angles is

14

:

4

. Find the measure of each angle.

Understand the problem: Step $1$ : Understand the problem and set up the equation. $\newline$ Supplementary angles add up to $180$ degrees. The ratio of the angles is $14:4$ , which simplifies to $7:2$ . Let's denote the larger angle as $7x$ and the smaller angle as $2x$ . $\newline$ Equation: $7x + 2x = 180$
Solve for x: Step $2$ : Solve for x. $\newline$ Combine like terms: $9x = 180$ $\newline$ Divide both sides by $9$ to isolate $x$ : $x = \frac{180}{9}$ $\newline$ $x = 20$
Find angle measures: Step $3$ : Find the measures of the angles. $\newline$ Larger angle = $7x = 7 \times 20 = 140$ degrees $\newline$ Smaller angle = $2x = 2 \times 20 = 40$ degrees

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