Question

The three angles of a triangle are in the ratio 1 : 2 : 3. What is the largest angle in the triangle?

• A. 30${}^{\circ }$
• B. 90${}^{\circ }$
• C. 60${}^{\circ }$
• D. 120${}^{\circ }$

Answer 1

The correct option is B 90${}^{\circ }$

From Legendre's axiom, we know:
"The sum of angles of any triangle is a constant and is equal to
two right angles".

Let, the angles of the triangle be x${}^{\circ }$, 2x${}^{\circ }$ and 3x${}^{\circ }$
$\therefore$ x${}^{\circ }$ + 2x${}^{\circ }$ + 3x${}^{\circ }$ = 180${}^{\circ }$
$\Rightarrow$ 6x${}^{\circ }$ = 180${}^{\circ }$
$\Rightarrow$ x${}^{\circ }$ = 30${}^{\circ }$

$\therefore$ Largest angle = 3x = 90${}^{\circ }$