Question

If the angles of a triangle are in the ratio $2:3:4$, find the three angles.

• A. ${80}^o,{120}^o,{160}^o$
• B. ${20}^o,{30}^o,{40}^o$
• C. ${40}^o,{60}^o,{80}^o$
• D. None of these

Answer 1

Answer: (C)

${40}^o,{60}^o,{80}^o$

The angles of a triangle are in the ratio $2:3:4$.
Let $x:y:z=2:3:4$.
Then, $x=2t,y=3t$ and $z=4t$.

We know, by angle sum property, the sum of all angles of a triangles is ${180}^0$.
$⟹$ $2t+3t+4t={180}^o$
$⟹$ $9t={180}^o$
$⟹$ $t={20}^o$.

Therefore, $x=2\times {20}^o={40}^o;y=3\times {20}^o={60}^o;z=4\times {20}^o={80}^o$.

Hence, option $C$ is correct.