In the figure, AD intersects BE at C. If x = 100, what is the value of y?

Explanation

Choice C is correct. The problem gives that x = 100, which is the measure of one angle in triangle ABC. To find the other two angles, note that the sum of angles in a triangle is always 180°. Therefore, the other two angles in triangle ABC must add up to 80°. If angle ABC is given as 20°, then angle BCA is 60° (180° - 100° - 20°). Because angle BCA and angle DCE are vertical angles, angle DCE is also 60°. In triangle CDE, we apply the triangle angle sum property again: 180° - 60° - 40° = 80°, giving us angle CDE as 80°. The other options represent common mistakes, such as assuming angles are right angles without justification or confusing different angles within the triangles.