Final answer:
Angles BCE and CED are same-side interior angles since they are on the same side of the transversal and inside the parallel lines BC and ED. Their measures add up to 180 degrees, confirming they are supplementary.
Step-by-step explanation:
The student has asked to identify the angle relationship between angles BCE and CED, given that lines BC and ED are parallel, and there are two transversals AE and EC intersecting these parallel lines. Angle ABC is 70 degrees, and angle CED is 30 degrees.
Since angle BCE is adjacent to angle ABC, and given that ABC is 70 degrees, we can deduce that angle BCE is 110 degrees because they form a straight line, which adds up to 180 degrees. Now, if we look at the relationship between BCE (110 degrees) and CED (30 degrees), we can see that these angles do not fall into the categories of alternate interior, alternate exterior, or corresponding angles because they are on the same side of the transversal and are non-adjacent. Therefore, angles BCE and CED are same-side interior angles.
The characteristic of same-side interior angles is that they are supplementary when the lines are parallel, which means their measures add up to 180 degrees. In this case, 110 degrees (BCE) plus 70 degrees (CED) equals to 180 degrees.