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In the triangle ABC, which of the following must be true ?

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In the triangle ABC, which of the following must be true ?

by vinni.k » Thu May 09, 2013 12:18 am
In the triangle ABC, which of the following must be true ?

I. x > 50
II. AC < 10
III. AB > 10

A. I only
B. III only
C. I and II only
D. I and III only
E. I, II, and III

Answer is C

Please explain.

Thanks & Regards
Vinni
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by Atekihcan » Thu May 09, 2013 1:44 am
(x + x + (x - 15)) = 180 ---> 3x = 195 --> x = 65
So, clearly I is true.

Now, BC = 10 and it's opposite angle measures 65 degrees.
Opposite angle of AC measures (65 - 15) = 50 degrees.
So, AC must be less than BC.
So, II is also true.

And, AB = BC = 10
So, clearly III is not true.

Answer : C
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by hemant_rajput » Thu May 09, 2013 3:00 am
vinni.k wrote:In the triangle ABC, which of the following must be true ?

I. x > 50
II. AC < 10
III. AB > 10

A. I only
B. III only
C. I and II only
D. I and III only
E. I, II, and III

Answer is C

Please explain.

Thanks & Regards
Vinni

3x - 15 = 180 ( sum of angle of triangle)

x = 65.

so 1 is true.
now ac is opposite to angle x -15 so it will be less than the side opp to angle x, which is having length of 10.
so 2 is also true.
now ab = bc = 10( isosceles triangle)
so 3 is definitely not true.

answer is c.
I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.
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