Question

the measure of an angle is 4 times the measure of its supplement. find the measures of both angles. the measures of both angles are ​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​° and ​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​°.

Explanation:

Step1: Define the angles

Let one angle be $x$. Its supplement is $180 - x$.

Step2: Set up the equation

Given that $x = 4(180 - x)$.

Step3: Solve the equation

Expand: $x=720 - 4x$.
Add $4x$ to both sides: $x + 4x=720$, so $5x = 720$.
Divide both sides by 5: $x=\frac{720}{5}=144$.

Step4: Find the supplement

The supplement is $180 - 144 = 36$.

Answer:

144, 36