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

[vinni.k]

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

[Atekihcan]

(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

[hemant_rajput]

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.