Question

an angle measures 48° 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 other angle is \(x + 48\). Since complementary angles sum to \(90^{\circ}\), we have \(x+(x + 48)=90\).

Step2: Simplify the equation

Combine like terms: \(2x+48 = 90\).

Step3: Solve for \(x\)

Subtract \(48\) from both sides: \(2x=90 - 48\), so \(2x = 42\). Then divide by \(2\): \(x=\frac{42}{2}=21\).

Step4: Find the other angle

The other angle is \(x + 48=21+48 = 69\).

Answer:

\(21^{\circ}\) and \(69^{\circ}\)