Question

In a $△$ABC, if 2$\angle$A = 3$\angle$B = 6$\angle$C, determine $\angle$A, $\angle$B and $\angle$C

Answer 1

We have, 2$\angle$A = 3$\angle$B = 6$\angle$C

$\Rightarrow$ $\angle$A = $\angle$B = $\angle$C

Let $\angle$A = 3x, $\angle$B = 2x and $\angle$C = x. Then,

$\angle$A + $\angle$B + $\angle$C = ${180}^{\circ }$

3x + 2x + x = ${180}^{\circ }$

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

x = ${30}^{\circ }$

Hence angles of the triangle are

$\angle$A = ${90}^{\circ }$, $\angle$B = ${60}^{\circ }$, $\angle$C = ${30}^{\circ }$