Question

If four angle at a point are in ratio $1:2:3:6$, then find all the angles.

• A. ${24}^o,{72}^o,{90}^o,{144}^o$
• B. ${30}^o,{60}^o,{90}^o,{180}^o$
• C. ${40}^o,{60}^o,{120}^o,{80}^o$
• D. ${25}^o,{75}^o,{90}^o,{170}^o$

Answer 1

Answer: (B)

${30}^o,{60}^o,{90}^o,{180}^o$

Let one angle be x. Then other angles are x, 2x, 3x and 6x.
As, we know, Sum of angle at point is ${360}^o$.
$\therefore x+2x+3x+6x={360}^o$
$12x={360}^o$
$x=\frac{{360}^o}{12}={30}^o$
Then angles are ${30}^o$
$2x={60}^o$
$3x={90}^o$
$6x={180}^o$