Question

An angle measures 110° less than the measure of its supplementary angle. What is the measure of each angle?

Answer 1

Answer: the angle is 35 degrees

The supplementary angle is 145 degrees

Step-by-step explanation:

Supplementary angles are angles whose sum is 180 degrees. This means that if angle x and angle y are supplementary, then the sum of angle x + angle y is 180 degrees.

The given angle measures 110° less than the measure of its supplementary angle.

Let the angle be x degrees and the supplementary angle be y degrees. This means that.

x = y - 110

Recall, sum of supplementary angles is 180 degrees. Therefore,

x + y = 180 - - - - - - - - 1

Substituting x = y - 110 into equation 1, it becomes

y - 110 + y = 180

2y -110 = 180

2y = 180 + 110 = 290

y = 290/2 = 145 degrees

x = y - 110 = 145 - 110

x = 35 degrees