Question

the measure of the supplement of an angle is three times the measure of the angle. find the measures of the angle and its supplement. measure of the angle = measure of the angles supplement =

Explanation:

Step1: Define the angle and its supplement

Let the measure of the angle be $x$. The measure of its supplement is $180 - x$.

Step2: Set up the equation

Given that the measure of the supplement of an angle is three times the measure of the angle, so $180 - x=3x$.

Step3: Solve the equation for $x$

Add $x$ to both sides: $180=3x + x$, which simplifies to $180 = 4x$. Then divide both sides by 4: $x=\frac{180}{4}=45$.

Step4: Find the measure of the supplement

Substitute $x = 45$ into the formula for the supplement. The supplement is $180 - 45=135$.

Answer:

measure of the angle = 45
measure of the angle's supplement = 135