Question

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)°
.Correct answers:
105°

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the largest angle in the triangle, we need to add up all the angles and set them equal to 180 degrees (the total sum of angles in a triangle).

(x-20) + (3x+3) + (2x-7) = 180

Now, we can combine like terms and solve for x:

6x - 24 = 180
6x = 204
x = 34

Now, we can substitute x back into each angle to find their measures:

Angle 1: (x-20) = 34 - 20 = 14 degrees
Angle 2: (3x+3) = 3(34) + 3 = 105 degrees
Angle 3: (2x-7) = 2(34) - 7 = 61 degrees

Thus, the largest angle in the triangle is 105 degrees.