Using Properties of Angles to Solve Problems

Question

Two angles are complementary. The larger angle is 30∘ larger than the smaller angle. Find the measure of both angles, and separate your answers with a comma.

Answer 1

Hi Kiara M

Smaller angle is 30 degrees

Larger angle is 60 degrees

Please see below

Complementary angles total 90

If I understand your description above, the larger angle is 30 degrees more than the smaller angle.

Let x = your smaller angle

Let x + 30 = your larger angle

Since they are complementary angles then

larger angle + smaller angle = 90

x + x + 30 = 90

Combine like terms

2x + 30 = 90

Subtract 30 from both sides of the equation

2x = 90 - 30

2x = 60

Divide both sides by 2

x = 30

Checking

Smaller angle = x = 30

Larger angle = x + 30 = 30 + 30 = 60

30 + 60 = 90

Hope this helps.