Question

an angle measures 83.6° less than the measure of its complementary angle. what is the measure of each angle? ° and ° submit

Explanation:

Step1: Set up the equations

Let the angle be \(x\) and its complementary angle be \(y\).
We know that \(x + y=90^{\circ}\) (complementary angles sum to \(90^{\circ}\)) and \(x=y - 83.6^{\circ}\)

Step2: Substitute and solve

Substitute \(x=y - 83.6^{\circ}\) into \(x + y=90^{\circ}\)
\((y - 83.6^{\circ})+y=90^{\circ}\)
\(2y-83.6^{\circ}=90^{\circ}\)
\(2y=90^{\circ}+ 83.6^{\circ}\)
\(2y=173.6^{\circ}\)
\(y=\frac{173.6^{\circ}}{2}=86.8^{\circ}\)

Step3: Find the other angle

Substitute \(y = 86.8^{\circ}\) into \(x=y - 83.6^{\circ}\)
\(x=86.8^{\circ}-83.6^{\circ}=3.2^{\circ}\)

Answer:

\(3.2^{\circ}\) and \(86.8^{\circ}\)