Respuesta :

semsee45

Answer:

The angle is 75°

Its complement is 15°

Its supplement is 105°

Step-by-step 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°

Angle be y

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

ATQ

[tex]\\ \rm\Rrightarrow 4(90-y)=180-y-45[/tex]

[tex]\\ \rm\Rrightarrow 360-4y=135-y[/tex]

[tex]\\ \rm\Rrightarrow 3y=225[/tex]

[tex]\\ \rm\Rrightarrow y=75[/tex]

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