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)
The Triangle Angle Sum Theorem states that the sum of the measures of the interior angles of a triangle is always 180 degrees.
Therefore, we can write an equation based on this theorem:
(x-20) + (3x+3) + (2x-7) = 180
Simplify the equation by combining like terms:
6x - 24 = 180
6x = 204
x = 34
Now, we can substitute x back into each angle measure to find the largest angle:
(34-20) = 14 degrees
(3(34)+3) = 105 degrees
(2(34)-7) = 61 degrees
The largest angle is 105 degrees.