A) An isosceles triangle.
B) An equilateral triangle.
C) A right angled triangle.
D) A right angled isosceles triangle.
Correct Answer: C
Solution :
Let the least angle be \[{{x}^{o}}\]. The greatest angle \[={{x}^{o}}+{{60}^{o}}\] Third angle \[=\frac{x+x+{{60}^{o}}}{2}=x+{{30}^{o}}\] We have, \[x+x+{{30}^{o}}+x+{{60}^{o}}={{180}^{o}}\] \[\Rightarrow \] \[3x+{{90}^{o}}={{180}^{o}}\,\,\Rightarrow \,\,x={{30}^{o}}\] \[\therefore \]The angles are \[{{30}^{o}},{{60}^{o}}\] and \[{{90}^{o}}\]. Since one of the angles is \[{{90}^{o}}\], the triangle formed is a right angled triangle.
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