use the triangle sum theorum to find the largerst angle meashers of (x-20) (3x+39) and (2x-7)

Answer 1

To find the largest angle measure, we need to compare the three angles and determine which one is the largest.

Let's denote the angles as follows:
Angle 1 = x-20
Angle 2 = 3x+39
Angle 3 = 2x-7

By the triangle sum theorem, the sum of the measures of any two angles in a triangle is greater than the measure of the third angle.

Therefore, we can write three inequalities:

Angle 1 + Angle 2 > Angle 3
(x-20) + (3x+39) > (2x-7)

4x + 19 > 2x - 7
2x > -26
x > -13

Angle 1 + Angle 3 > Angle 2
(x-20) + (2x-7) > (3x+39)

3x - 27 > 3x + 39
-27 > 39 (This is not possible.)

Hence, Angle 3 + Angle 2 > Angle 1
(2x-7) + (3x+39) > (x-20)

5x + 32 > x - 20
4x > -52
x > -13

So, the largest angle measure is Angle 2, which is given by:
Angle 2 = 3x + 39
Angle 2 = 3(-13) + 39
Angle 2 = -39 + 39
Angle 2 = 0

Therefore, the largest angle measure is 0 degrees.