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Find the measure of the exterior angle​

Find The Measure Of The Exterior Angle class=

Sagot :

renknee

Answer:

133°

Step-by-step explanation:

Exterior Angle Theorem states that the sum of the two remote interior angles is equal to the exterior angle of the triangle.

  • This means that 83 + x + 10 = 3x + 13, and we have to solve it algebraically.

Step 1: Combine like terms.

  • [tex](83+10) + x = 3x + 13[/tex]
  • [tex]93 + x = 3x + 13[/tex]

Step 2: Subtract x from both sides.

  • [tex]93 + x - x = 3x + 13 - x[/tex]
  • [tex]93 = 2x + 13[/tex]

Step 3: Subtract 13 from both sides.

  • [tex]93-13=2x+13-13[/tex]
  • [tex]80=2x[/tex]

Step 4: Divide both sides by 2.

  • [tex]80/2=2x/2[/tex]
  • [tex]x = 40[/tex]

Step 5: Plug in 40 in 3x + 13.

  • [tex]3(40) + 13[/tex]
  • [tex]120+13[/tex]
  • [tex]133[/tex]

Therefore, the answer is 133°.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

Answer:

133°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

3x + 13 is an exterior angle of the triangle , then

3x + 13 = x + 10 + 83 , that is

3x + 13 = x + 93 ( subtract x from both sides )

2x + 13 = 93 ( subtract 13 from both sides )

2x = 80 ( divide both sides by 2 )

x = 40

Then

exterior angle = 3x + 13 = 3(40) + 13 = 120 + 13 = 133°

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