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Which one of the following cannot be the ratio of angles in a right-angled triangle?

  1. $1:2:3$ 
  2. $1:1:2$ 
  3. $1 :3:6$ 
  4. None of these
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A) 1:2:3 - Let these angles equal x, 2x & 3x.                                

           By angle sum property of a triangle,   

             x+2x+3x = 6x = 180. 

               So, x = 30 & 2x =60 &  3x = 90. Hence, it is the ratio of angles in a right-angled triangle.

B) 1:1:2 - Let these angles equal x, x & 2x.                                

           By angle sum property of a triangle,   

             x+x+2x = 4x = 180. 

               So, x = 45 & x =45 &  2x = 90. Hence, it is the ratio of angles in a right-angled triangle.

C) 1:3:6 - Let these angles equal x, 3x & 6x.                                

           By angle sum property of a triangle,   

             x+3x+6x = 10x = 180. 

               So, x = 18 & 3x =54 &  6x = 108Hence, it is not the ratio of angles in a right-angled triangle.

Option C is the Correct Answer.

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