Use the triangle angle sum theorem to find the largest angle in a triangle with the angle measures of (x - 30) , (2x + 6), and (2x + 4)

84

10

86

180

1 answer

In a triangle, the sum of the three interior angles is always 180 degrees.

So, we can set up the equation:

(x - 30) + (2x + 6) + (2x + 4) = 180

Combine like terms:

5x - 20 = 180

Add 20 to both sides:

5x = 200

Divide by 5:

x = 40

Now, we can find the measures of the angles:

(40 - 30) = 10 degrees
(2(40) + 6) = 86 degrees
(2(40) + 4) = 84 degrees

Therefore, the largest angle is 86 degrees.