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)°

Answer 1

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°.