angles and arcs in circles

Question

anonymous · Answer

attachment

anonymous · Answer

@Directrix   ??

anonymous · Answer

Well, i'm not entirely sure about the answer since I'm a little fuzzy on arcs and circles, but first of all, is the diagram drawn to scale?

anonymous · Answer

i dont believe so.

directrix · Answer

I think this is the theorem you need.

anonymous · Answer

Alright I think I got it. The angles are created by to intersecting chords, making vertical angles, and vertical angles are equal, so you really only need to find the measure of one angle to figure out the other. Anyway, the measure of an angle formed by two intersecting chords is 1/2(marcAD + marcBC) (marc being measure of arc). So (86 + 96)/2=91 for the measure of angle AED. angle AEC in turn is 89.

anonymous · Answer

sorry for the long reply, I couldn't figure out the equation thing.

directrix · Answer

@chicagoblkhaks   Do the arithmetic. Then, we have to find <AEC which is the supplement of <AED. See attached file.

anonymous · Answer

sorry guys my computer needed to update. thanks for the help!!