Question

an angle measures 28° 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 \(x + 28\). Since complementary angles sum to \(90^{\circ}\), we have \(x+(x + 28)=90\).

Step2: Simplify the equation

Combine like terms: \(2x+28 = 90\).

Step3: Solve for \(x\)

Subtract \(28\) from both sides: \(2x=90 - 28\), so \(2x=62\). Divide both sides by \(2\): \(x = 31\).

Step4: Find the other angle

The other angle is \(x + 28=31+28 = 59\).

Answer:

\(31\) and \(59\)