Question

an angle measures 22° more than the measure of its complementary angle. what is the measure of each angle?

Explanation:

Step1: Define complementary angles

Complementary angles add up to 90°. Let the measure of the complementary - angle be \(x\) degrees. Then the measure of the given angle is \(x + 22\) degrees.

Step2: Set up an equation

Since the two angles are complementary, we have the equation \(x+(x + 22)=90\).

Step3: Simplify the equation

Combine like - terms: \(2x+22 = 90\).

Step4: Solve for \(x\)

Subtract 22 from both sides: \(2x=90 - 22=68\). Then divide both sides by 2: \(x = 34\).

Step5: Find the measure of the other angle

The other angle is \(x + 22\). Substitute \(x = 34\) into it, we get \(34+22 = 56\).

Answer:

34, 56