Are all the angles in triangle ABC less than 90 degrees?

Hi honchos,

manpreetsingh86's explanation is right on, but I do want to point out one error in it:

A 3/4/5 right triangle is NOT a 30/60/90 right triangle - those are 2 different triangles.

Here's another way to look at this question:

We're asked if all 3 angles in triangle ABC are less than 90 degrees. This is a YES/NO question.

Fact 1: AB < BC < AC

This tells us the relationship among the lengths of the 3 sides. We know that none of the sides are equal to one another, so none of the corresponding angles are equal to one another.

We could have....

...a 30/60/90 and the answer to the question would be NO.
...a 50/60/70 and the answer to the question would be YES.
Fact 1 is INSUFFICIENT

Fact 2: Angle ABC = 80

This tells us one of the angles, but we don't know if it's the biggest angle or not.

We could have...

a...10/80/90 and the answer to the question would be NO.
a...30/70/80 and the answer to the question would be YES.
Fact 2 is INSUFFICIENT

Combined, we know...
Angle ABC = 80
Angle ABC is across from AC
AB < BC < AC
The biggest angle is always across from the biggest side

Thus the biggest angle is 80, so the other 2 angles are BOTH less than 80.
The answer to the question is ALWAYS YES.
Combined, SUFFICIENT.

Final Answer:

GMAT assassins aren't born, they're made,
Rich