Use the Triangle Angle Sum Theorem to find the largest angle in a triangle with angle measures of (x−20)° , (3x+3)° , and (2x−7)° .(1 point)

Answer 1

To find the largest angle in a triangle, we need to consider the sum of all three angles.

Let x-20, 3x+3, and 2x-7 be the angle measures of the triangle.

According to the Triangle Angle Sum Theorem, the sum of the interior angles of a triangle is always 180 degrees.

Therefore, we can write the equation:
(x-20) + (3x+3) + (2x-7) = 180

Now, we can solve for x:
x - 20 + 3x + 3 + 2x - 7 = 180
6x - 24 = 180
6x = 204
x = 34

Now that we have found x, we can substitute it back into the angle measures:

Angle 1: x-20 = 34 - 20 = 14 degrees
Angle 2: 3x+3 = 3(34) + 3 = 105 degrees
Angle 3: 2x-7 = 2(34) - 7 = 61 degrees

Therefore, the largest angle in the triangle is 105 degrees.