Question

the measure of an angle is twenty - four times the measure of its supplementary angle. what is the measure of each angle? \\(\square^\circ\\) and \\(\square^\circ\\)

Explanation:

Step1: Define variables

Let the measure of the supplementary angle be \( x \) degrees. Then the measure of the other angle is \( 24x \) degrees.

Step2: Use supplementary angle property

Since supplementary angles add up to \( 180^\circ \), we have the equation \( x + 24x = 180 \).

Step3: Solve the equation

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

Step4: Find the other angle

The other angle is \( 24x = 24\times7.2 = 172.8 \).

Answer:

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