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 angles in a triangle is always 180 degrees.
Therefore, we need to 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, we can substitute the value of x back into the angle measures to find their values:
(x-20) = (34-20) = 14°
(3x+3) = (3*34+3) = 105°
(2x-7) = (2*34-7) = 61°
Therefore, the largest angle in the triangle is 105°.