Data Sufficiency

What is the measure of angle x in the figure provided, if BF and DE are parallel?

1) AC is perpendicular to BF

2) Triangle ABC is equilateral

Answer is C

Why answer cannot be B.

Thanks & Regards
Vinni

Vinni,

Here's my solution.

The answer is C

Statement 1 - AC is perpendicular to BF means the angle at F is 90 degrees. It does not give the angle at B. Hence insufficient.

Statement 2 - ABC is equilateral. Just proves A, B and C are 60 degrees. Still does not give me y - and I think where you are going wrong with this one is by assuming that BF is bisecting the angle. That cannot be assumed because the images are never drawn to scale.

COmbining Statement 1 and 2 - we know that AC is perpendicular to BF, making BF a bisector of the angle at B. Hence y is 30 and since BF and DE are parallel, x+a = 180. where a=y. Therefore x = 150.

I hope that helps you out.

Regards
Anup

anuprajan5 wrote:Vinni,

Here's my solution.

The answer is C

Statement 1 - AC is perpendicular to BF means the angle at F is 90 degrees. It does not give the angle at B. Hence insufficient.

Statement 2 - ABC is equilateral. Just proves A, B and C are 60 degrees. Still does not give me y - and I think where you are going wrong with this one is by assuming that BF is bisecting the angle. That cannot be assumed because the images are never drawn to scale.

COmbining Statement 1 and 2 - we know that AC is perpendicular to BF, making BF a bisector of the angle at B. Hence y is 30 and since BF and DE are parallel, x+a = 180. where a=y. Therefore x = 150.

I hope that helps you out.

Regards
Anup

Thanks Anup.

By statement (2) i am taking triangle DEC, where i have 90 degree angle, 60 degree angle because triangle BAC is equilateral, and y since BF||DE.

After adding 90+60+y=180
150+y=180
y=30

After that y+x=180
30+x=180
x=150

This is what i am doing. Am i assuming too much by statement (2) ?

Regards
Vinni

vinni.k wrote:
By statement (2) i am taking triangle DEC, where i have a 90 degree angle, 60 degree angle because triangle BAC is equilateral, and y since BF||DE.

The portion in red need not be true in statement 2.
It's possible that BF and DE are parallel to each other but both at a slant.

Vini,

Just as Gmayguruny said, BF and DE can be parallel at an angle. So we cannot assume that DE is at 90degrees.

Regards
Anup

Thank you so much Mitch and Anup. Now, i understand where i was making a mistake. You guys are the best.

Regards
Vinni