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

15° and 165°

Step-by-step explanation:

Step 1:

Let x and y denote the angles with x as the smaller angle and y as the larger angle

When 2 angles are supplementary, the sum of both the angles is 180 degrees.

Hence x + y = 180

Step 2:

Given that the larger angle is 15 more than 10 times the smaller angle

Hence y = 15 + 10 x

Step 3:

Solving for the 2 equations we have

11x = 165 = > x = 15

=> y = 180-15 = 165

Hence the 2 angles are 15 and 165 degrees.