Example #1:Two angles are supplementary. The smaller angle is 3 more than seven times x. The larger angle is 21 less than 11 times x. Find the measures of the angles.

Smaller angle = 7x + 3Larger angle = 11x – 21

7x + 3 + 11x – 21 = 180 18x – 18 = 180 18x = 198 x = 11

7(11) + 3 = 8011(11) – 21 =100

Supplementary means you need to add and set equal to 180.

Example #2:One angle is 40 more than twice x. Another angle is 50 less than 5 times x. These two angles are vertical angles. Find the measures of each angle.

When angles are vertical they are equal.

One angle = 2x + 40Another angle = 5x – 50

2x + 40 = 5x – 50 40 = 3x – 50 90 = 3x 30 = x

2(30) + 40 = 1005(30) – 50 = 100

Example #3:Two angles are complementary. The larger angle is 6 less than double the smaller angle. Find the measure of the larger angle.

This time you will need to define what x is equal to. Then since the angles are complementary, add them together and set them equal to 90.

We know little about the smaller angle so set x equal to the smaller angle.

Smaller angle = xLarger angle = 2x – 6

x + 2x – 6 = 90 3x – 6 = 90 3x = 96 x = 32

2(32) – 6 = 58

Example #4:The smaller of two angles is 30 more than half the larger angle. If the angles are supplementary, what is the measure of the larger angle?

This time you will also need to define what x is equal to. Then since the angles are supplementary, add them together and set them equal to 180.

We know little about the larger angle so set x equal to the larger angle.

Larger angle = xSmaller angle = 0.5x + 30

x + 0.5x + 30 = 180 1.5x + 30 = 180 1.5x = 150 x = 100

The larger angle is 100.

Example #5:One vertical angle is 10 less than twice x. The other vertical angle is 4 times the quantity of x minus 35. Find the angles.

When angles are vertical they are equal.

One angle = 2x – 10The other angle = 4(x – 35)

2x – 10 = 4(x – 35)2x – 10 = 4x – 140 -10 = 2x – 140 130 = 2x 65 = x

2(65) – 10 = 1204(65 – 35) = 120