Question

the measure of an angle is thirty - five times the measure of its complementary angle. what is the measure of each angle? \\(\square^{\circ}\\) and \\(\square^{\circ}\\)

Explanation:

Step1: Define variables

Let the measure of the complementary angle be \( x \) degrees. Then the measure of the other angle is \( 35x \) degrees.

Step2: Use complementary angle property

Complementary angles add up to \( 90^\circ \), so we have the equation \( x + 35x = 90 \).

Step3: Solve the equation

Combine like terms: \( 36x = 90 \). Then divide both sides by 36: \( x=\frac{90}{36}=2.5 \).

Step4: Find the other angle

The other angle is \( 35x = 35\times2.5 = 87.5 \).

Answer:

\( 87.5^\circ \) and \( 2.5^\circ \)