Question

The angles of a triangle are in the ratio $1:2:3.$ The measure of the largest angle is
(a) ${30}^{\circ }$
(b) ${60}^{\circ }$
(c) ${90}^{\circ }$
(d) ${120}^{\circ }$

Answer 1

The correct option is (c): ${90}^{\circ }$

Given: Angles of a triangle in the ratio $1:2:3$

Let the common multiplying factor to these angles be $x.$

so, the angles will be $x,2x,$ and $3x.$

We know that the sum of all the angles of a triangle is equal to ${180}^{\circ }$.

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

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

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

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

so, Largest angle $=3x=3\times 30={90}^{\circ }$