Question

An angle's supplement is nine times of its complementary angle. Find the measure of the angle, the complement of the angle,and the supplement of the angle. Answer and Explain please

Answer 1

Measure of required angle = 78.75° , measure of complementary angle = 11.25° and measure of supplementary angle = 101.25°

Explanation:

let assume measure of required angle = x

since sum of angle and its supplement is 180°

so x + supplement of x = 180

⇒ supplement of x = 180 - x

since sum of angle and its complement is 90

so x + complement of x = 90

⇒ complement of x = 90 - x

Form given information

supplement of x = 9 × ( complement of x)

⇒180 - x = 9 × ( 90 - x )

⇒ 180 - x = 810 - 9x

⇒ -x + 9x = 810 - 180

⇒ 8x = 630

⇒ x = 630/8 = 78.75°

complement of x = 90 - x = 90 - 78.75° = 11.25°

and supplement of x = 180 - 78.75 = 101 .25°

we can recheck our solution by multiplying complement by 9 , that is 11.25 × 9 = 101.25 which is same as supplement. Hence our solution is correct.

So we can conclude that measure of required angle = 78.75° , measure of complementary angle = 11.25° and measure of supplementary angle = 101.25°