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)
According to the Triangle Angle Sum Theorem, the sum of the angles in a triangle is 180 degrees.
Therefore, we have the equation:
(x-20) + (3x+3) + (2x-7) = 180.
Simplifying the equation:
6x - 24 = 180.
Adding 24 to both sides:
6x = 204.
Dividing by 6:
x = 34.
Now we can substitute x back into the angle measures to find the largest angle.
The angle measures are: (34-20)°, (3(34)+3)°, and (2(34)-7)°.
Simplifying:
14°, 105°, and 61°.
Therefore, the largest angle is 105°.