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: Define variables

Let the measure of the supplementary angle be \( x \) degrees. Then the measure of the given angle is \( 59x \) degrees.

Step2: Use supplementary angle property

Since supplementary angles add up to \( 180^\circ \), we have the equation \( x + 59x = 180 \).

Step3: Solve the equation

Combine like terms: \( 60x = 180 \). Then divide both sides by 60: \( x=\frac{180}{60}=3 \).

Step4: Find the measures of the angles

The supplementary angle is \( x = 3^\circ \). The given angle is \( 59x = 59\times3 = 177^\circ \).

Answer:

\( 3^\circ \) and \( 177^\circ \)