Question

Four times the complement of an angle is 45 less than its supplement. Find the measures of all 3 <‘s

Answer 1

Angle be y

• It's complement angle=90-y
• Supplementary angle=180-y

ATQ

`\\ \rm\Rrightarrow 4(90-y)=180-y-45`

`\\ \rm\Rrightarrow 360-4y=135-y`

`\\ \rm\Rrightarrow 3y=225`

`\\ \rm\Rrightarrow y=75`

Answer 2

The angle is 75°

Its complement is 15°

Its supplement is 105°

Explanation:

Complementary angles: Two angles whose measures add to 90°

Supplementary angles: Two angles whose measures add up to 180°

Let x = unknown angle

⇒ complementary angle = 90 - x

⇒ supplementary angle = 180 - x

Four times the complement of an angle is 45 less than its supplement:

⇒ 4(90 - x) = (180 - x) - 45

⇒ 360 - 4x = 135 - x

⇒ 225 = 3x

⇒ x = 75°

⇒ complementary angle = 90 - 75 = 15°

⇒ supplementary angle = 180 - 75 = 105°