Question

an angle measures 19.8° more than the measure of its complementary angle. what is the measure of each angle?

° and
°

Explanation:

Step1: Let the measure of the complementary angle be \(x\)

Let the measure of the complementary angle be \(x\). Then the measure of the given angle is \(x + 19.8\)

Step2: Use the property of complementary angles

Since the sum of complementary angles is \(90^{\circ}\), we have the equation \(x+(x + 19.8)=90\)
Simplify the left - hand side: \(2x+19.8 = 90\)
Subtract \(19.8\) from both sides: \(2x=90 - 19.8=70.2\)
Divide both sides by \(2\): \(x=\frac{70.2}{2}=35.1\)

Step3: Find the measure of the given angle

The measure of the given angle is \(x + 19.8\). Substitute \(x = 35.1\) into it, we get \(35.1+19.8 = 54.9\)

Answer:

\(35.1\) and \(54.9\)