Question

an angle measures 56° more than the measure of its complementary angle. what is the measure of each angle? ° and °

Explanation:

Step1: Set up variables

Let the measure of the complementary angle be \(x\). Then the measure of the other angle is \(x + 56\).

Step2: Use the property of complementary angles

Since complementary angles sum to \(90^{\circ}\), we have the equation \(x+(x + 56)=90\).
Simplify the left - hand side: \(2x+56 = 90\).
Subtract 56 from both sides: \(2x=90 - 56\), so \(2x=34\).
Divide both sides by 2: \(x = 17\).

Step3: Find the measure of the other angle

The other angle is \(x + 56\). Substitute \(x = 17\) into it, we get \(17+56=73\).

Answer:

\(17^{\circ}\) and \(73^{\circ}\)