Question

The measure of the supplement of an angle is seven times as large as the measure of its complement find the measure of the angle, supplement, and complement.

Answer 1

Answer: original angle = 75°

Its supplement 105°

Its complement = 15°

Explanation:

We know that,

• Sum of supplementary angles is 180 degrees.
• Sum of complementary angles is 90 degrees.

Let x be the original angle , then its supplement = 180° - x

its complement = 90° - x

As per given,

180° - x = 7(90° - x)

⇒ 180° - x = 630° - 7x

⇒ 7x- x = 630° -180°

⇒ 6 x = 450°

⇒ x = 75° [divide both sides by 6]

So, original angle = 75°

Its supplement = 180° - 75° = 105°

Its complement = 90° -75° = 15°

Hence, original angle = 75°

Its supplement 105°

Its complement = 15°