Answer:
Measure of required angle = 78.75° , measure of complementary angle = 11.25° and measure of supplementary angle = 101.25°
Step-by-step 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°
