Question

angle measures 34° 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 \(x + 34\). Since complementary angles sum to \(90^{\circ}\), we have \(x+(x + 34)=90\).

Step2: Solve the equation

Simplify the left - hand side: \(2x+34 = 90\).
Subtract 34 from both sides: \(2x=90 - 34\), so \(2x = 56\).
Divide both sides by 2: \(x=\frac{56}{2}=28\).

Step3: Find the other angle

The other angle is \(x + 34\). Substitute \(x = 28\), we get \(28+34 = 62\).

Answer:

\(28\) and \(62\)