Use the Triangle Angle Sum Theorem to find the largest angle in a triangle with angle measures of (x−20)° , (3 x+3)° , and (2x−7)° .(1 point)
The Triangle Angle Sum Theorem states that the sum of the measures of the angles in a triangle is always 180°.
So, we can set up an equation:
(x−20)° + (3x+3)° + (2x−7)° = 180°
Combine like terms:
6x - 24 = 180
Add 24 to both sides:
6x = 204
Divide by 6:
x = 34
Now, plug in x = 34 to find the measures of the angles:
Largest angle = 3x + 3
= 3(34) + 3
= 102 + 3
= 105°
Therefore, the largest angle in the triangle is 105°.