Question

An angle measures 30° more than the measure of its complementary angle. What is the measure of each angle?

Answer 1

To solve for the two complementary angles where one is 30° more than the other, we set up an equation based on the total sum of complementary angles being 90°, yielding the angles as 30° and 60°.

Step-by-step explanation:

To determine the measure of two complementary angles where one angle measures 30° more than the other, we will use the property that the sum of complementary angles is 90°. Let's designate x as the measure of the smaller angle. Therefore, the larger angle is x + 30°. The equation will be setup as: x + (x + 30°) = 90°.

Combining like terms, we get 2x + 30° = 90°. Subtracting 30° from both sides, 2x = 60°. Dividing both sides by 2, we find x = 30°. So, the smaller angle is 30° and the larger angle, being 30° more, is 60°.

Thus, the complementary angles are 30° and 60°.

Answer 2

60 degrees and 30 degrees

Step-by-step explanation:

If you really want, you can set up a system of equations using the given information. X can the larger angle and Y can be the smaller angle.

x + y = 90

x = y + 30

In reality, this is not necessary for such a simple problem. Some trial and error testing would help you figure this out much faster.