Respuesta :

Angle C= 98°

Explanation:

First, find angle T, which will be 180°-130° (Angle T=50°)

Now you can work out for x
You know that all the angles in a triangle add up to 180°, which means that 50+x+(3x+2)=180°
Change subjects in order to find the value of x first
x+3x=180-50-2
4x=128
x=32

Now that you found the value of x, substitute it into the value of angle C
Angle C= 3x+2
Angle C= 3(32)+2
Angle C=98°
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Answer:

m∠C = 98°

Step 1: Derive an Equation

To solve this problem, we will use what is called the Exterior Angle Theorem. This states that in a triangle, the measure of an exterior angle is equal to the sum of the measures of its 2 corresponding remote interior angles.

  • Exterior angle - an angle formed by the extension of 1 side of the triangle
  • Remote interior angles - the 2 angles that don't share a vertex with the exterior angle

In this case, the exterior angle is ∠T (the obtuse one) and the remote interior angles are ∠C and ∠Y. Therefore, m∠T = m∠C + m∠Y.

Substituting the given measures into the equation, we get:

[tex]3x+2+x=130[/tex]

Step 2: Solve the Equation

[tex]3x+2+x=130[/tex]

[tex]4x+2=130[/tex] (Combine like terms)

[tex]4x=128[/tex] (Subtract 2 from both sides to isolate [tex]x[/tex])

[tex]x=32[/tex] (Divide both sides by 4 to get rid of [tex]x[/tex]'s coefficient)

Step 3: Answer the Question

We now know what [tex]x[/tex] is. Therefore, m∠C = [tex]3*32+2=\bf 98 \textdegree[/tex].

To learn more about the Exterior Angle Theorem, check out the following questions:

  • https://brainly.com/question/17147409
  • https://brainly.com/question/6330929

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