Question

two angles are supplementary. the measure of one is 20% of the measure of the other. find the measures of both angles.

Explanation:

Step1: Set up variables

Let one angle be $x$ and the other be $y$.

Step2: Use supplementary - angle property

Since the two angles are supplementary, $x + y=180^{\circ}$.

Step3: Use the given ratio

Given that $x = 0.2y$.

Step4: Substitute and solve

Substitute $x = 0.2y$ into $x + y=180^{\circ}$, we get $0.2y+y = 180^{\circ}$. Combining like - terms, $1.2y=180^{\circ}$. Then $y=\frac{180^{\circ}}{1.2}=150^{\circ}$.

Step5: Find the other angle

Substitute $y = 150^{\circ}$ into $x = 0.2y$, we get $x=0.2\times150^{\circ}=30^{\circ}$.

Answer:

$30^{\circ}$ and $150^{\circ}$