Question

the measure of an angle is seventeen times the measure of its supplementary angle. what is the measure of each angle?

Explanation:

Step1: Let the measure of the angle be $x$ degrees.

The measure of its supplementary angle is $(180 - x)$ degrees.

Step2: Set up the equation based on the given relationship.

We know that $x = 17(180 - x)$.

Step3: Expand the right - hand side of the equation.

$x=3060 - 17x$.

Step4: Add $17x$ to both sides of the equation.

$x + 17x=3060$, so $18x = 3060$.

Step5: Solve for $x$.

$x=\frac{3060}{18}=170$.

Step6: Find the measure of the supplementary angle.

The supplementary angle is $180 - 170 = 10$.

Answer:

The measure of the angle is $170^{\circ}$ and the measure of its supplementary angle is $10^{\circ}$