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 relationship

Let the measure of the angle be $x$. Its supplement is $180 - x$. Given that $180 - x=3x$.

Step2: Solve the equation

Add $x$ to both sides of the equation $180 - x=3x$. We get $180=3x + x$, which simplifies to $180 = 4x$.

Step3: Find the value of $x$

Divide both sides of $180 = 4x$ by 4. So $x=\frac{180}{4}=45$.

Step4: Find the measure of the supplement

The supplement of the angle $x$ is $180 - x$. Substitute $x = 45$ into it, we get $180-45 = 135$.

Answer:

The measure of the angle is $45^{\circ}$, and the measure of its supplement is $135^{\circ}$