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Two angles are supplementary. The measure of the larger angle is 28 more than 3 times the measure of the smaller angle.
Find the measures of both angles.

Answer :

  • Let smaller one be x
  • Larger is 3x+28

ATQ

[tex]\\ \rm\longmapsto 3x+28+x=180[/tex]

[tex]\\ \rm\longmapsto 4x+28=180[/tex]

[tex]\\ \rm\longmapsto 4x=152[/tex]

[tex]\\ \rm\longmapsto x\approx 38[/tex]

  • 3x+28=180-38=142

Given ↷

  • Given angles are supplementary
  • The measure of the larger angle is 28 more than 3 times the measure of the smaller angle

To find↷

  • Measures of both angles

Solution ↷

Let's assume that ,

x is the smaller angle

3x+28 is the larger angle

then,

ATQ,

x + 3x+28 = 180°

4x +28 = 180°

4x = 180°-28°

4x = 152°

x = 38°

putting the value of x in the larger angle

⇢3x +28 = 3 x 38° +28° = 142°

hence , the measure of the smaller angle is 38° & the larger one = 142°

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