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 5°. the measure of the larger angle is □°.

Explanation:

Step1: Recall complementary angles sum

Complementary angles sum to \(90^\circ\). Let the angles be \(x\) and \(17x\) (since ratio is \(1:17\)).

Step2: Set up equation

\(x + 17x = 90\)
\(18x = 90\)

Step3: Solve for x (smaller angle)

\(x=\frac{90}{18}=5\) (matches given smaller angle)

Step4: Find larger angle

Larger angle is \(17x = 17\times5 = 85\)

Answer:

The measure of the larger angle is \(85^\circ\).