Question

an angle measures 59.6° more than 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 \(x + 59.6^{\circ}\). Since complementary angles sum to \(90^{\circ}\), we have the equation \(x+(x + 59.6^{\circ})=90^{\circ}\).

Step2: Solve the equation for \(x\)

Combine like - terms: \(2x+59.6^{\circ}=90^{\circ}\).
Subtract \(59.6^{\circ}\) from both sides: \(2x=90^{\circ}-59.6^{\circ}=30.4^{\circ}\).
Divide both sides by 2: \(x = 15.2^{\circ}\).

Step3: Find the measure of the other angle

The other angle is \(x + 59.6^{\circ}\). Substitute \(x = 15.2^{\circ}\), we get \(15.2^{\circ}+59.6^{\circ}=74.8^{\circ}\).

Answer:

\(15.2\) and \(74.8\)