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)° .(1 point)

Answer 1

According to the Triangle Angle Sum Theorem, the sum of the angles in a triangle is always 180 degrees.

Therefore, we can write the equation:

(x-20)° + (3x+3)° + (2x-7)° = 180°

Now, let's solve this equation for x:

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

6x - 24 = 180

Adding 24 to both sides:

6x = 204

Dividing both sides by 6:

x = 34

Now, we can substitute x = 34 back into the original equation to find the angle measures:

(x-20)° = (34-20)° = 14°

(3x+3)° = (3(34)+3)° = 105°

(2x-7)° = (2(34)-7)° = 61°

Therefore, the largest angle measure is 105°.