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
[tex]x+3(90-x)=270-2x[/tex]
[tex]90-x+180-x=270-2x[/tex]
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
