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In triangle ABM ( M - point where AC intersects BD)
AB = 1/2 AM (coz ABD and BCD are congruent triangles)
so L BAM = 60
Hence X = 90 - 60 = 30 ( right angle triangle)

the figure ABCD is a rhombus with equals sides and equal diagonals. so ABC is an equilateral triangle with all angles are 60. the intersection of AC is the midpoint and bisects ABC. so ABD is 30.
_________________

If your mind can conceive it and your heart can believe it, have faith that you can achieve it.

My understanding is AB=BC=CD are talking about line BC and line CD, not the arcs. Therefore we can get the equalateral trangle and the 30 degree.
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

I think you cannot assume that BC is a straight line and call the figure a rhombus.

Although the answers come the same in both cases ( I got 30 too ) I think your approach is a little flawed.

but all sides are equal. the diagonals are perpendicular. AB=AC=AC=radii. it must be a rhombus or a equilateral parallelogram. otherwise BC wouldnt equal CD.
_________________

If your mind can conceive it and your heart can believe it, have faith that you can achieve it.

I think you cannot assume that BC is a straight line and call the figure a rhombus.

Although the answers come the same in both cases ( I got 30 too ) I think your approach is a little flawed.

but all sides are equal. the diagonals are perpendicular. AB=AC=AC=radii. it must be a rhombus or a equilateral parallelogram. otherwise BC wouldnt equal CD.

Chris, I didnt understand, can you explain why BC cannot equal CD ?

All,
The confusion is whether BC and CD are arcs or straight lines. The problem can be solved assuming either.

I solved it assuming BC and CD are arcs because they are shown as arcs and not as straight lines.

What happens if we get somethign like this in the exam ? What do you assume then ?
_________________

ash
________________________
I'm crossing the bridge.........

is there some data missing in this figure like if AD is perpedicular then X will be 30 degrees as ABC and BCD are equilateral trianglels

The secant is bisected because the arc itself is bisected. Therefore the line will be a perpendicular from center to secant. This has to be deduced.

Data provided is sufficient.

I'm not sure I understand how it can be assumed that BD is perpendicular to AC

OK.. this is a rule, any line that bisects a chord is perpendicular to it.

Try deducing it yourself. The line bisects the chord and creates two congruent triangles. The angles that hit the chord will therefore be equal to each other.

Angle on the chord = 180/2 = 90
_________________

ash
________________________
I'm crossing the bridge.........

All, The confusion is whether BC and CD are arcs or straight lines. The problem can be solved assuming either.

I solved it assuming BC and CD are arcs because they are shown as arcs and not as straight lines.

You can't assume the BC and CD in AB=BC=CD (given in the stem) are arcs ashkg. AB should be less then arc BC and arc CD if AB is going to be equal to segment BC and segment CD.
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.