Question

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

Explanation:

Step1: Set up the equation

Let the measure of the complementary angle be \(x\). Then the measure of the other angle is \(24x\). Since complementary angles sum to \(90^{\circ}\), we have \(x + 24x=90\).

Step2: Solve the equation

Combine like terms: \(25x = 90\). Then \(x=\frac{90}{25}=3.6\).

Step3: Find the measure of the other angle

The other angle is \(24x\). Substitute \(x = 3.6\) into \(24x\), we get \(24\times3.6 = 86.4\).

Answer:

\(3.6^{\circ}\) and \(86.4^{\circ}\)