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# In triangle ABC below, what is the length of side BC? 1,

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Manager
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In triangle ABC below, what is the length of side BC? 1, [#permalink]  01 Nov 2007, 09:40
In triangle ABC below, what is the length of side BC?

1, Line segment AD has length 6

2, x = 36

Answer is a, Statement (1) Alone is sufficient. But don't know how, please explain.

Regards,
Pinal
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Manager
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ok you know that <BDC and <ADB ar esupplementary angles so that means <ADB = 180-2x

now you konw that all the angles in ADB have to addup to 180
so <ABD = 180 - (x + 180-2x) = x

so since <ABD = <DAB = x, if you know AD is 6, then you also know that BD is 6 too.

so <BCD = 2x corresponds to the side length of x, the side length of BC corresponds to angle <BDC, which is also 2x, thus is would be 6 too.
CEO
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U must know b/f doing this problem certain rules of triangles and angles.

Lets say the triangle to the far left has angle measures of x z and y.

z is the angle at the top and y is the right bottom angle.

knowing line rules, y+2x=180 also x+z+y=180

y=180-2x ---> x+z-2x+180 = 180 so z-x=0. This means that z-x are the same value.

I just did this to show what the following rule is: the outside value (2x) is equal to angles x+z. This rule always holds for triangles and you should know it!

Now since z=x we know that BD is 6, which corresponds to angle z and since angle z=x. angle x corresponds to length of 6 as well.

S2: is garbage.

A.
Current Student
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GMATBLACKBELT wrote:
U must know b/f doing this problem certain rules of triangles and angles.

Lets say the triangle to the far left has angle measures of x z and y.

z is the angle at the top and y is the right bottom angle.

knowing line rules, y+2x=180 also x+z+y=180

y=180-2x ---> x+z-2x+180 = 180 so z-x=0. This means that z-x are the same value.

I just did this to show what the following rule is: the outside value (2x) is equal to angles x+z. This rule always holds for triangles and you should know it!

Now since z=x we know that BD is 6, which corresponds to angle z and since angle z=x. angle x corresponds to length of 6 as well.

S2: is garbage.

A.

GREAT explanation. Kudos
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Re: [#permalink]  08 Feb 2008, 09:17
GMATBLACKBELT wrote:
U must know b/f doing this problem certain rules of triangles and angles.

Lets say the triangle to the far left has angle measures of x z and y.

z is the angle at the top and y is the right bottom angle.

knowing line rules, y+2x=180 also x+z+y=180

y=180-2x ---> x+z-2x+180 = 180 so z-x=0. This means that z-x are the same value.

I just did this to show what the following rule is: the outside value (2x) is equal to angles x+z. This rule always holds for triangles and you should know it!

Now since z=x we know that BD is 6, which corresponds to angle z and since angle z=x. angle x corresponds to length of 6 as well.

S2: is garbage.

A.

Statement 2 cannot derive the value of a side because we only have only angles. we need a defined side to derive another side.
_________________

You tried your best and you failed miserably. The lesson is 'never try'. -Homer Simpson

Re:   [#permalink] 08 Feb 2008, 09:17
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