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) $$ Skip to navigation
The Triangle Angle Sum Theorem states that in any triangle, the sum of the angles is always equal to 180 degrees.
Therefore, we have the equation:
(x - 20) + (3x + 3) + (2x - 7) = 180
Simplifying the left side of the equation, we get:
6x - 24 = 180
Adding 24 to both sides of the equation, we get:
6x = 204
Dividing both sides of the equation by 6, we get:
x = 34
Now we can substitute the value of x back into the angle measures to find the largest angle:
(3x + 3)° = (3(34) + 3)° = 105°
Therefore, the largest angle in the triangle is 105 degrees.