Respuesta :

YuriSmith

Question:

∠1 and ∠2 are supplementary angles. m∠1 is 4y+7, and m∠2 is 9y+4. Find m∠2.

Solution:

The sum of supplementary angle is 180°

First, solve for the value of y.

  • ∠1 + ∠2 = 180°
  • (4y + 7) + (9y + 4) = 180°
  • 13y + 11 = 180°
  • 13y = 180° - 11
  • 13y = 169/13
  • y = 13°

Then, plug and substitute the value y = 13 to find the m∠2.

  • m∠2
  • 9y + 4
  • 9(13) + 4
  • 117 + 4
  • 121

Answer:

  • The angle of m∠2 is 121
akposevictor

The measure of angle 2 is 121 degrees.

Given:

[tex]m\angle1=4y+7\\m\angle2=9y+4[/tex]

Recall: Supplementary angles are angles whose sum equals [tex]180^{o}[/tex]

To solve this problem, create an equation to find the value of x:

Thus:

[tex]m\angle1 +m\angle2=180[/tex]

Therefore:

[tex](4y+7)+(9y+4) = 180\\[/tex]

Solve for y:

[tex]4y+7+9y+4 = 180\\\\[/tex]

Add like terms:

[tex]13y+11 = 180\\\\[/tex]

Subtract 11 from both sides

[tex]13y+11 - 11= 180 - 11\\13y = 169[/tex]

Divide both sides by 13

[tex]\frac{13y}{13} = \frac{169}{13} \\y = 13[/tex]

Find the m∠2 by substituting [tex]y = 13[/tex] into [tex]9y +4[/tex]

[tex]m\angle= 9(13)+4\\m\angle = 121^{o}[/tex]

Therefore, m∠2 = 121 degrees.

Learn more about supplementary angles here:

https://brainly.com/question/18175975

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