Question

In AABC, mZA = (3x)', mZB = (3x + 10), and mZC = (4x - 30). Find m2C.

A. 14°
B. 20°
C. 26°
D. 50°

Answer 1

The measure of
`\(\angle C\)` is 50 degrees. The answer is D. 50°.

In triangle ABC, the sum of all interior angles is always 180 degrees. Therefore, we can write the equation:

`\[ \angle A + \angle B + \angle C = 180^\circ \]`

Now, substitute the given angle measures:

`\[ (3x) + (3x + 10) + (4x - 30) = 180^\circ \]`

Combine like terms:

`\[ 10x - 20 = 180^\circ \]`

Add 20 to both sides:

`\[ 10x = 200^\circ \]`

Divide by 10:

`\[ x = 20^\circ \]`

Now that we know the value of x, we can find
`\(\angle C\)`:

`\[ \angle C = 4x - 30 = 4(20) - 30 = 50^\circ \]`

So, the measure of
`\(\angle C\)` is 50 degrees. The answer is D. 50°.