Question

the measure of an angle is seventeen times the measure of its complementary angle. what is the measure of each angle? input box° and input box° submit

Explanation:

Step1: Define variables

Let the measure of the complementary angle be \( x \) degrees. Then the measure of the angle is \( 17x \) degrees.

Step2: Use complementary angle property

Since complementary angles add up to \( 90^\circ \), we have the equation \( x + 17x = 90 \).

Step3: Solve the equation

Combine like terms: \( 18x = 90 \). Then divide both sides by 18: \( x=\frac{90}{18}=5 \).

Step4: Find the angle measures

The complementary angle is \( x = 5^\circ \), and the angle is \( 17x = 17\times5 = 85^\circ \).

Answer:

\( 5^\circ \) and \( 85^\circ \)