A) An isosceles triangle.
B) An equilateral triangle.
C) A right angled triangle.
D) A right angled isosceles triangle.
Correct Answer: C
Solution :
(c): Mind of a Mathematician: Let \[\angle les\] be \[x-\alpha ,\text{ }x,\text{ }x,+\text{ }\alpha \] (we can choose such variables intelligently ; by making such choice, middle angle is automatically average of first and third angles): Now difference \[=(x+\alpha )-(x-\alpha )=2\alpha =60{}^\circ \] Also sum of \[\angle les\] \[=x-\alpha +x+x+\alpha \] \[=3x=180{}^\circ \] \[=x=60{}^\circ \] \[=x-\alpha =30{}^\circ \] \[=x=60{}^\circ \] \[=x+\alpha =90{}^\circ \] \[=\angle right\,\,\Delta \,\,le.\]
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