Question

The sum of the measures of a complement and supplement of an angle is 144. Find the measure of the angle.

Answer 1

63o

Explanation:

given angle is ∠A

then complementary angle is ∠C

and supplementary angle is ∠S

so A + C = 90 => C = 90 - A

A + S = 180 => S = 180 - A

since C + S = 144

=> (90 - A) + (180 - A) = 144

270 - 2A = 144

2A = 270 - 144

2A = 126

A = 63

Answer 2

63°

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 sum of the measures of the complement and supplement of x is 144:

⇒ (90° - x°) + (180° - x°) = 144°

⇒ 90° + 180° - x° - x° = 144°

⇒ 270° - 2x° = 144°

⇒ 270° - 2x° + 2x° = 144° + 2x°

⇒ 270° = 144° + 2x°

⇒ 270° - 144° = 144° + 2x° - 144°

⇒ 126° = 2x°

⇒ 126° ÷ 2 = 2x° ÷ 2

⇒ 63° = x°

⇒ x° = 63°

Therefore, the measure of the angle is 63°.