Answer:
x = 5
Explanation:
The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles.
In the given problem, the exterior angle is < B, and the non-adjacent interior angles are < D and < C.
Given that:
< B = 12x + 8
< D = 8x + 8
< C = 20°
Set up the following formula to solve for x:
(8x + 8) + 20 = 12x + 8
Combine like terms:
8x + 28 = 12x + 8
Subtract 8 from both sides:
8x + 28 - 8 = 12x + 8 - 8
8x + 20 = 12x
Subtract 8x from both sides:
8x - 8x + 20 = 12x - 8x
20 = 4x
Divide both sides by 4 to solve for x:
20/4 = 4x/4
5 = x
Therefore, x = 5.