Question

the measure of an angle is fifty - nine times the measure of its supplementary angle. what is the measure of each angle?

Explanation:

Step1: Let the measure of the supplementary - angle be \(x\) degrees.

The measure of the angle is \(59x\) degrees.

Step2: Recall the property of supplementary angles.

Supplementary angles add up to 180 degrees. So, \(x + 59x=180\).

Step3: Combine like - terms.

\(60x = 180\).

Step4: Solve for \(x\).

Divide both sides of the equation by 60: \(x=\frac{180}{60}=3\).

Step5: Find the measure of the other angle.

The other angle is \(59x\), so \(59\times3 = 177\).

Answer:

3 and 177