Using the Triangle Sum Theorem, find the measure of the largest angle in a triangle with measures of (x - 20), (3x + 3) , and (2x - 7).

Answer 1

The Triangle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees.

So, we can set up an equation using the measures of the angles:

(x - 20) + (3x + 3) + (2x - 7) = 180

Combining like terms, we get:
6x - 24 = 180

Adding 24 to both sides:
6x = 204

Dividing by 6:
x = 34

Now, we can substitute the value of x back into the measures of the angles to find the largest angle:
2x - 7 = 2(34) - 7 = 68 - 7 = 61

Therefore, the largest angle in the triangle measures 61 degrees.