Question

the ratio of the measures of two complementary angles is 1:17. find the measure of each angle.

the measure of the smaller angle is $square^circ$.

Explanation:

Step1: Define variables for angles

Let the measures of the two complementary angles be \( x \) and \( 17x \) (since their ratio is \( 1:17 \)).

Step2: Use complementary angles property

Complementary angles add up to \( 90^\circ \), so we set up the equation: \( x + 17x = 90 \).

Step3: Solve the equation

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

Answer:

The measure of the smaller angle is \( 5^\circ \).