Question

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

• A. $2:3:5$
• B. $1:3:6$
• C. $1:2:3$
• D. $1:3:4$

Answer 1

The correct option is B $1:3:6$

$\left(A\right)$ $2:3:5$

Let the angles be $2x,3x$ and $5x$

$\Rightarrow$ $2x+3x+5x={180}^o$

$\Rightarrow$ $10x={180}^o$

$\Rightarrow$ $x={18}^o$

$\Rightarrow$ $2x={36}^o,3x={54}^o$ and $5x={90}^o$

Hence, this ratio is right.

$\left(B\right)$ $1:3:6$

Let the angles be $x,3x$ and $6x$

$\Rightarrow$ $x+3x+6x={180}^o$

$\Rightarrow$ $10x={180}^o$

$\Rightarrow$ $x={18}^o$

$\Rightarrow$ $x={18}^o,3x={54}^o$ and $6x={108}^o$

So, this ratio is wrong.

$\left(C\right)$ $1:2:3$

Let the angles be $x,2x$ and $3x$

$\Rightarrow$ $x+2x+3x={180}^o$

$\Rightarrow$ $6x={180}^o$

$\Rightarrow$ $x={30}^o$

$\Rightarrow$ $x={30}^o,2x={60}^o$ and $3x={90}^o$

Hence, this ratio is right.

$\left(D\right)$ $1:3:4$

Let the angles be $x,3x$ and $4x$

$\Rightarrow$ $x+3x+4x={180}^o$

$\Rightarrow$ $8x={180}^o$

$\Rightarrow$ $x={22.5}^o$

$\Rightarrow$ $x={22.5}^o,3x={67.5}^o$ and $4x={90}^o$

Hence, this ratio is right.

$\therefore$ $1:3:6$ cannot be the ratio of angles in right angled triangle.