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Are all the angles of triangle ABC smaller than 90 degrees?

1. AB < BC <AC> =>Angle ABC> AngleCAB> AngleBCA but all of them might be less than 90 also or AngleABC might be more than 90So it is insuffcient 2. Angle ABC = 80 degrees => Doesn't give much option about other angle so insuff

from one and two AngleABC =80>Angle CAB>Angle BCA so all are less than 90 hence both are required to answer hence

I. Insuf: the longest side should be less than the sum of the 2 shortest sides: AC < AC + BC
8 < 6 + 3 --> we have one angle that is >90
8 < 8 + 8 --> All angles = 60
Insuff

II. Insuff, Angle ABC = 80 --> the sum of other 2 angles = 100, so it can be 50 + 50 or 95 + 5

Are all the angles of triangle ABC smaller than 90 degrees?

1. AB < BC < AC 2. Angle ABC = 80 degrees

What can we infer from 1 and why is it insuff??

I think it is a good question, my approach would be to draw the figure according to the given statement.

Then it is clear from statement that one of the angle should be Greater than 90deg.

Just draw the figures and it is clear that in one case Angle can be greater than 90deg, as shown in the first two triangles. Therefore, Statement 1 is insufficient.

From statement 2, if we know one angle is 80deg, then the third triangle is possible.

Did you guys tried by drawing the figure or is there better faster approach for GMAT?

When you draw an 80 deg angle..the other two angles have to be less that 90 deg. If you draw a 90 deg angle and an 80 deg angle, the other two sides will not meet. We don't need statement 1. Try drawing the figure..

This is a problem from m23. I think there is an error in the answer choice C.

Anyone can explain if otherwise? Thanks

Sum of all angles of a triangle = 180 degree. So considering one angle equals to 80 degrees, we can have other two angles as 90 degrees and 10 degrees. It it true that the lines making 10 degree angle will be too long, but finally they will meet at certain point. Also if you are saying that the lines making 80 degree and 90 degree angles with one of the sides of the triangle, will not meet, then these two lines must be parallel (?!?). It is not possible for two parallel lines to make angles of different measures with another line. I will suggest you the same, try drawing the figure...

Are all the angles of triangle ABC smaller than 90 degrees?

1. AB < BC < AC 2. angle(ABC) = 80

official explanation: Statement (1) by itself is insufficient.

Statement (2) by itself is insufficient.

Statements (1) and (2) combined are sufficient. S1 and S2 gives that angle(ABC) is the largest angle. Thus, the other two angles are smaller than 80 degrees and the answer to the question is "yes".

in a triangle ABC, if angle(ABC) is the largest angle, then side AB cannot be the largest side since its adjacent to angle(ABC).

I believe the answer should be E and not B for the following reason:

For a triangle ABC,

set angle(ABC) = 80, set angle(ACB) = 90, then angle(BAC) must equal 10 and AB<BC<AC. Therefore the answer to the question is NO.

set angle(ABC)=80, set angle(ACB) = 89, then angle(BAC) must equal 11 and AB<BC<AC. Therefore the answer to the question is YES.

the boundary conditions for the angles based on statements 1 and 2 are: (from statement 2, angle(ABC) = 80)

0 < angle(BAC) < 50 50 < angle(ACB) < 100

Therefore B is incorrect and the answer should be E. _________________

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If both are combined AC is the largest side, ABC is the largest angle and 80*. hence the other two angle has to be lessthan 80* or 90*. hence C is the answer
_________________

When you draw an 80 deg angle..the other two angles have to be less that 90 deg. If you draw a 90 deg angle and an 80 deg angle, the other two sides will not meet. We don't need statement 1. Try drawing the figure..

This is a problem from m23. I think there is an error in the answer choice C.

Anyone can explain if otherwise? Thanks

Sum of all angles of a triangle = 180 degree. So considering one angle equals to 80 degrees, we can have other two angles as 90 degrees and 10 degrees. It it true that the lines making 10 degree angle will be too long, but finally they will meet at certain point. Also if you are saying that the lines making 80 degree and 90 degree angles with one of the sides of the triangle, will not meet, then these two lines must be parallel (?!?). It is not possible for two parallel lines to make angles of different measures with another line. I will suggest you the same, try drawing the figure...

Read explanation given above.. I too though this way but its wrong.. Trick here is not in imagination. Its in understanding the naming conventions
_________________

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