Question

In the following diagram it is known that AB=AC, BAC = 30°, and EAC = 75°. Explain why AE must be parallel to BC

Answer 1

AE is parallel to BC because alternate internal angles are equal

How to find the alternate internal angles

From the given description, the given triangle is an isosceles triangle

Solving for base angles of isosceles triangle, x

x + x + 30 = 180

2x = 180 - 30

2x = 150

x = 75

ABC = ACB = x = 75 degrees

And ACB = EAC = 75° (alternate internal; angles are equal)