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
The Triangle Angle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees.
Therefore, we can set up an equation using the given angle measures:
(x-20) + (3x+3) + (2x-7) = 180
We can simplify this equation by combining like terms:
6x - 24 = 180
Adding 24 to both sides, we get:
6x = 204
Dividing by 6:
x = 34
Now that we have determined the value of x, we can substitute it back into the angle measures to find the largest angle:
3x + 3 = 3(34) + 3 = 102 + 3 = 105
Therefore, the largest angle in the triangle is 105 degrees.