Question

Two complementary angles in the ratio 5:7. What is the measure of the smaller angle?

Answer 1

The measure of the smaller angle in a set of complementary angles with a ratio of 5:7 is 37.5 degrees.

Step-by-step explanation:

To find the measure of the smaller angle in a set of complementary angles with a given ratio, we need to divide the ratio by the sum of its parts and then multiply the result by 90 degrees.

In this case, the ratio is 5:7, so the smaller angle would be (5 / (5 + 7)) * 90 degrees. Simplifying this expression gives us the measure of the smaller angle.

Smaller angle = (5 / (5 + 7)) * 90 degrees
= (5 / 12) * 90 degrees
= 37.5 degrees

Answer 2

So,

Complementary angles are angles which add together to make 90°.

To find the value of one unit in the ratio 5:7, take these steps:
Add the number of units.
5 + 7 = 12

Divide 90° by 12.
90/12 = 7.5°

The smaller angle is "worth" 5 units.
7.5 * 5 = 37.5°