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by feeet » Sun Apr 12, 2009 12:50 am
how can I solve it?
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Source: — Data Sufficiency |
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by mals24 » Sun Apr 12, 2009 3:12 am
Let angle ABD = y

Using the exterior angle theorem:
x+y = 2x
y=x

AD = BD = 6

Hence, AD=BD=BC=6

So St 1 is suff.

St 2 just gives you degree measures of the angles and we have no information about any of the lengths of the sides

So st 2 is insuff

For more information on exterior angle theorem check:
https://en.wikipedia.org/wiki/Exterior_angle_theorem
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by Ian Stewart » Sun Apr 12, 2009 7:19 am
Or without using the exterior angle theorem:

-- angle ADB is 180 - 2x, because ADC is a straight line;

-- using that, angle ABD must be x, because the angles in triangle ADB must add to 180.

So triangle ADB is isosceles, and the length of AD is equal to the length of BD, which is equal to BC, since triangle BDC is isosceles. So if AD is 6, so is BC.
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