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tatuchka [14]
2 years ago
7

Find angle C, can someone help me with this please?

Mathematics
2 answers:
stiks02 [169]2 years ago
6 0
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°
sergij07 [2.7K]2 years ago
5 0

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 <u>exterior angle</u> is equal to the sum of the measures of its 2 corresponding <u>remote interior angles</u>.

  • <u>Exterior angle</u> - an angle formed by the extension of 1 side of the triangle
  • <u>Remote interior angles</u> - 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, <u>m∠T = m∠C + m∠Y</u>.

Substituting the given measures into the equation, we get:

3x+2+x=130

Step 2: Solve the Equation

3x+2+x=130

4x+2=130 (Combine like terms)

4x=128 (Subtract 2 from both sides to isolate x)

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

Step 3: Answer the Question

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

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

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