Question

the measure of an angle is twenty - four times the measure of its supplementary angle. what is the measure of each angle? ° and °

Explanation:

Step1: Set up the equation

Let the measure of the supplementary angle be \(x\). Then the measure of the angle is \(24x\).
Since supplementary angles sum to \(180^{\circ}\), we have \(x + 24x=180\).

Step2: Solve the equation

Combine like terms: \(25x = 180\).
Divide both sides by 25: \(x=\frac{180}{25}=7.2\).

Step3: Find the measure of the other angle

The other angle is \(24x\). Substitute \(x = 7.2\) into \(24x\), we get \(24\times7.2 = 172.8\).

Answer:

\(7.2^{\circ}\) and \(172.8^{\circ}\)