If AE=ED and AB=BC=CD

[nipunjindal91]

If AE=ED and AB=BC=CD, what is the value of x in the figure above?

105

130

135

140

145

Please someone help me solve the above question.
P.S. the source is HULT GMAT test.

[tim]

I have no idea what "HULT GMAT test" is, but without any additional information I have no reason to believe it is one we're allowed to discuss here. Please provide more information about this source so we can help you. If you don't, we'll have to delete the question.

Also, before we help with this question, we'd like you to show some effort of your own. What did you try on this question? Where did you get stuck?

[nipunjindal91]

Hi Tim,

I came across this question in a practice test by Hult International Business school powered by The Economist.
Please let me know in case you require any other information.

I tried doing the question by joining the vertices A & D, A & C and B & D. Using the property of triangles (angles opposite to equal sides are equal), I could figure out that the angles EDA & EAD are equal to 52.5 degree each.. After that I got stuck.

Thanks.

[tim]

This is very difficult for a GMAT question (one of the reasons you should be careful about which sources you use for practice questions). Can I assume this question was in a free practice test?

Because the angle at E is 75 degrees, that means the arc from A to D is 150 degrees. Because there are three congruent chords marking off this 150 degrees, each of them marks off 50 degrees. This means that arc BD is 100 degrees, so taking the "long way around" from B to D gives us 260 degrees (360-100). Angle x is half of this, or 130.