a side of the triangle below has been extended to form an exterior angle of 66 degrees. find the value of x

Let's use the exterior angle theorem here, which states that the sum of two opposite interior angles is equal to the sum of the exterior angle.
Therefore, we have:
x + 19 = 66
Let's solve for x.
Subtract 19 from both sides:
x + 19 - 19 = 66 - 19
x = 47°
ANSWER:
x = 47°