Question

Two angles are supplementary. The larger angle is 15 more than 10 times the smaller angle. Find the measure of each angle.

Can someone explain this and help me get the answer

Answer 1

The angles are 165 and 15

Explanation:

Supplementary angles whose sum is 180°

Let A and B be the two supplementary angles.

Let A be the larger angle and B the smaller angle.

From the question, we were told that the large angle (A) is 15 more than 10 times the smaller angle ie

A = 15 + 10B

We can solve for the value of A and B by doing the following:

A + B = 180

But A = 15 + 10B

15 + 10B + B = 180

Collect like terms

10B + B = 180 — 15

11B = 165

Divide both side by the coefficient of B i.e 11

B = 165/11

B = 15

A = 15 + 10B

A = 15 + 10(15)

A = 15 + 150

A = 165

The angles are 165 and 15