Question

If the measure of one angle is five times its complement, find the measure of its supplement.

Answer 1

Answer:

let x be the complement

5x=90-x

6x=90

x=15

supplement

180-x

180-15

165

Answer 2

Given,

An angle is 5 times its complement.

To find,

The measure of its supplement.

Solution,

It is given here that an angle is 5 times its complement.

Firstly, let the complementary angle of this angle be x. Then the original angle will be 5x.

Now, since the sum of the complementary angles is = 90°.

For, the given angles,

5x + x = 90

6x = 90

x = 15°

We have found the complementary angle x = 15, so the original angle will be,

5x = 5(15) = 75°

Now, we have to find supplementary of this angle. Let the supplementary angle be y.

Since the sum of the supplementary angles is = 180°

So,

75 + y = 180°

⇒ y = 180 - 75

⇒ y = 105°.

Therefore, the measure of the supplement of the given angle will be 105°.