Describe and correct the error in finding the measure of the angle

Sorry, it's late, and I'm a bad explainer.

The error is adding (2x-12) with x and 30. This is wrong because you are adding the angles inside the triangle and you are assuming that (2x - 12) is the unlabeled angle INSIDE the triangle, when it is the exterior angle/outside of the triangle.

A straight line is also 180°.

(2x - 12) + ? = 180

30 + x + ? = 180

If you look at the equations, and put parentheses around 30 + x, (30 + x) and (2x - 12) should be the SAME NUMBER. So you could set them equal to each other to find x. (or you could also look at the picture and see that they both need/are missing the same angle)

2x - 12 = 30 + x

x = 42

Now you plug 42 into the exterior angle equation

2(42) - 12 = 84 - 12 = 72°

Step-by-step explanation:

Notice that the triangles already have one pair of congruent sides and one pair of congruent angles.

Now, remember that the SAS congruence theorem refers to the congruence between two pairs of corresponding sides and one pair of corresponding angles. That means we just need another pair of congruent sides.

Therefore, the additional information we need is , because they are corresponding sides which make triangles ABC and ADE congruent.