Question

show that when the measure of an angle is added to three times the angle's complement, the result is equal to the sum of the anle's complment and the angle's supplement.

Answer 1

Answer with Step-by-step explanation:

Let x be the angle

We have to show that when the measure of an angle is added to three times the angle's complement , the result is equal to the sum of the angle;s complement and the angle' s supplement.

Angle's complement =90-x

(by definition of complementary angles)

Therefore, the angle's supplement=180-x ( By definition of supplement angles )

According to question

`x+3(90-x)=270-2x`

`90-x+180-x=270-2x`

Hence, when the measure of an angle is added to three times the angle's complement , the result is equal to the sum of the angle's supplement.

Hence, proved