a. The Triangle Sum Theorem states that the sum of the interior angles in a triangle is equal to 180 degrees.
Let's assume that the three angles in the triangle are A, B, and C.
The equation that represents the sum of the angles in the triangle is:
A + B + C = 180 degrees
b. Let's say the value of x represents one angle in the triangle.
Using the equation from part a, we can write:
x + (2x + 10) + (3x - 10) = 180
Combine like terms:
x + 2x + 3x + 10 - 10 = 180
6x = 180
Now, we can solve for x by dividing both sides of the equation by 6:
(6x)/6 = 180/6
x = 30
So, the value of x is 30.