Question

The measure of an angle is seventeen times the measure of its supplementary angle. What is the measure of each angle? (In degrees)

a) 85 degrees and 95 degrees
b) 75 degrees and 105 degrees
c) 85 degrees and 170 degrees
d) 80 degrees and 100 degrees

Answer 1

To solve this problem, set up an equation using x and y as the measures of the angles. Substitute x = 17y and x + y = 180, solve for y, and find x using x = 17y.the correct answer is option c)85 degrees and 170 degrees

Step-by-step explanation:

To solve this problem, we need to set up an equation. Let x be the measure of one angle and y be the measure of its supplementary angle. We know that the measure of an angle is seventeen times the measure of its supplementary angle, so we can write the equation x = 17y. We also know that supplementary angles add up to 180 degrees, so we can write the equation x + y = 180.

Substituting x = 17y into the second equation, we get 17y + y = 180. Combining like terms, we have 18y = 180. Dividing both sides by 18, we find y = 10. Plugging this value back into x = 17y, we get x = 17(10) = 170.

Therefore, the measure of each angle is 170 degrees and 10 degrees.