I solved this question in the following way:

At first sight you must see that <DBC and <CDB have the same angle.

So the length of BD must be equal to BC.

The rephrased question is then as followings: What is BD?First analyse the given picture as 1 triangle (ABC)The angle of B would be : 180 - Angle A - Angle C = 180 - 3x

Secondly look at the triangle (BCD).The angle of B would be now: 180 - Angle C - Angle D = 180 - 4x

To find the the Angle of B in the Triangle of ABD , subtract these two equations:180 - 3x - 180 --4x(=+)= x

Since Angle <ABD = <BDA

The length of AD must be equal to BD. ( Because they have the same angle )

AD=BD=BC

If you know the length of AD or BD , you have sufficient information to answer the question.

(1) Sufficient , you now know the length of AD.

(2) You know nothing about any length , clearly insufficient.

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