Question

In the diagram below, D is a point on segment CE such that segments AD and BE are parellel and point A is not on segment BC. Line segments AD and BC intersect at point P.

If angle CAD = 67 degrees, then what is angle CBE?

Answer 1

Explanation:

Since segment AD and BE are parallel, we can use the Alternate Interior Angles Theorem to solve this. According to this theorem, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are equal. Since angle CAD = 67 degrees, angle DBE is also equal to 67 degrees.

Now, if we look at the diagram, angle DBE is supplementary to angle CBE, meaning that the two angles add up to 180 degrees. Therefore, angle CBE = 180 degrees - 67 degrees = 113 degrees.