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Lunna [17]
3 years ago
14

An angle's supplement is nine times of its complementary angle. Find the measure of the angle, the complement of the angle,and t

he supplement of the angle. Answer and Explain please
Mathematics
1 answer:
Masja [62]3 years ago
8 0

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°


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