Use the triangle angle sum theory to find the largest angle in a triangle with the measures of (x-20), (3x+3), and (2x-7)

Question

Use the triangle angle sum theory to find the largest angle in a triangle with the measures of (x-20), (3x+3), and (2x-7)

Answer 1

According to the triangle angle sum theory, the sum of the three angles in a triangle is always 180 degrees.

So, we have:

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

Combining like terms, we get:

6x - 24 = 180

Adding 24 to both sides:

6x = 204

Dividing by 6:

x = 34

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

Largest angle = 3x + 3 = 3(34) + 3 = 102 + 3 = 105 degrees

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