The measure of an angle is fourteen times the measure of its complementary angle. What is the measure of each angle?

Answer 1

Complementary angles - Angles that have a sum of 90 degrees

Not to be confused with…

Supplementary angles - Angles that have a sum of 180 degrees

We can solve this by defining both angles algebraicly in terms of the smaller angle

Smaller angle = (x)

Larger angle = 14*(x) or simply 14x

Smaller angle + Larger angle = 90

(x) + 14(x) = 90

Combining like terms you get the next step…

15x = 90

Then we isolate the variable…

15x/15 = 90/15

X = 6

This means, per the parameters of the initial question, that…

The smaller angle is 6 degrees.

The larger, complementary angle is fourteen times the measure of the smaller angle or 14(6) degrees = 84 degrees.

Answer 2

x= 14(90-x) The angle x = 14 times its complementary angle, 90-x.

x= 1260 -14x

15x = 1260

x = 1260/15= 420/5= 84 degrees

90-x= 90-84 = 6 degrees

Answer 3

Hi Stephanie,

Complementary angles add to 90 degrees, so set the smaller angle equal to x and the larger angle equal to 14x. Together, these add to 90, so:

x + 14x = 90

15x = 90

x=6

First angle is 6 degrees. Second angle is:

14*6 = 84

Angle measures are 6 degrees, 84 degrees. I hope this helps.