Question

the measure of a supplement of an angle exceeds 10 times the measure of its complement by 9. Find the measure of the angle

Answer 1

81°

Explanation:

Let the angle be x. Then,

• complementary angle = 90 - x
• supplementary angle = 180 - x

According to question,

=> 180 - x - 10(90 - x) = 9

=> 180 - x - 900 + 10x = 9

=> 9x - 720 = 9

=> 9x = 729

=> x = 81

The measure of the angle is 81° (ans)

Answer 2

81°

Explanation:

Definitions

Complementary angles: Two angles whose measures sum to 90°.

Supplementary angles: Two angles whose measures sum to 180°.

Define the unknown angle

• Let x be the unknown angle.

Therefore:

• Complement of x = 90° - x°
• Supplement of x = 180° - x°

If the measure of the supplement exceeds 10 times the measure of its complement by 9:

⇒ supplement = 10 × complement + 9

⇒ (180 - x) = 10(90 - x) + 9

⇒ 180 - x = 900 - 10x + 9

⇒ 180 - x = 909 - 10x

⇒ 180 - x + 10x = 909 - 10x + 10x

⇒ 180 + 9x = 909

⇒ 180 + 9x - 180 = 909 - 180

⇒ 9x = 729

⇒ 9x ÷ 9 = 729 ÷ 9

⇒ x = 81

Therefore, the measure of the angle is 81°.