Question

In a $△$ABC, if 2$\angle$A = 3$\angle$B = 6$\angle$C, then $\angle$A, $\angle$B, $\angle$C are respectively _________.

• A. ${30}^{\circ }$, ${60}^{\circ }$, ${90}^{\circ }$
• B. ${90}^{\circ }$, ${60}^{\circ }$ , ${30}^{\circ }$
• C. ${30}^{\circ }$, ${90}^{\circ }$, ${60}^{\circ }$
• D. None of these

Answer 1

The correct option is B

${90}^{\circ }$, ${60}^{\circ }$ , ${30}^{\circ }$

Given, 2$\angle$A = 3$\angle$B = 6$\angle$C

Consider

2$\angle$A = 3$\angle$B = 6$\angle$C

$\angle$B = $\frac{2}{3}\angle A$

$\angle$C = $\frac{2}{6}\angle A$

In any triangle, we know that the sum of all the angles of a triangle is equal to 180°, (Angle Sum Property)

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

$\angle$A + $\frac{2}{3}$$\angle$A + $\frac{2}{6}$$\angle$A = ${180}^{\circ }$

$\frac{12}{6}$$\angle$A = ${180}^{\circ }$

$\angle$A = ${90}^{\circ }$

$\angle$ B = $\frac{2}{3}$$\angle$A = $\frac{2}{3}$ $\times$ 90° = 60°

$\angle$ C = $\frac{2}{6}$$\angle$A = $\frac{2}{6}$ $\times$ 90° = 30°