Triangle ABC is isosceles but not equilateral. Out of AB, BC and AC

Question

Triangle ABC is isosceles but not equilateral. Out of AB, BC and AC which are the two equal sides?

(1) Exterior angle at B is acute.

(2) Exterior angle at A is obtuse.

Archit3110 · Answer

#1
for an isosceles triangle the two interior angles are equal and third angle >90 ; eg 45:45;90
given 
Exterior angle at B is acute but not sure of other two sides would have exterior angle as obtuse and interior as acute so sufficeint ; as its given that triangle is isosceles..
sufficient

#2:
angle a interal angle <90 ; which all other internal angles may or may not be <90 not clear ; insufficient
IMO A

ocelot22 · Answer

Draw triangle ABC. Draw line segments jutting out from vertices A and B to form external angles. Label the internal angles as x,y,z as below

MusicCzar · Answer

In a Triangle , there can be only one Obtuse angle.
If one angle is >90 (obtuse), then the other two angles has to be acute (<90) since sum of all the angles in the triangle is 180.
Statement 1: exterior angle at B is acute. Hence Angle B, is obtuse. If angle B is obtuse, the other two angles A and B are acute. Since it is an Isosceles triangle, Angle A= Angle B , and sides opposite to these two angles are equal. hence Sufficient.
Statement 2: This statement tells that Angle A is acute ie, Angle A <90. Angle B as well as angle C can also be acute. We do not know which two angles are equal. Hence Insufficient.

Loser94 · Answer

Sum of 3 angles = 180in triangle 
 ANd sum of 2 interior angle is eqaul to exterior angle of remaining side 
So, 
(1) Exterior angle at B is acute. 
 So , angle B is obtuse >90
This gives us sum of angle A+C= <90=Ext angle B 
so this case is only possible when angle side opposite to a and c are eqaul

(2) Exterior angle at A is obtuse.
interior angle a <90 
nothing can be answered

Answer A

Thanks

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Triangle ABC is isosceles but not equilateral. Out of AB, BC and AC

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