Question

If the angles of a triangle are in the ratio 2 : 3 : 4, what is the difference between the largest angle and the smallest angle?

• A. 20${}^{\circ }$
• B. 40${}^{\circ }$
• C. 60${}^{\circ }$
• D. 80${}^{\circ }$

Answer 1

The correct option is B 40${}^{\circ }$

From Legendre's theorem, we know that the sum of all the angles of a triangle is constant and is equal to two right angles.
Let the angles of the traingle be 2x, 3x and 4x.
$\therefore$ 2x + 3x + 4x = 180${}^{\circ }$

$\Rightarrow$ 9x = 180${}^{\circ }$
$\Rightarrow$ x = 20${}^{\circ }$
$\therefore$ The angles are:
2x = 2(20${}^{\circ }$) = 40${}^{\circ }$
3x = 3(20${}^{\circ }$) = 60${}^{\circ }$
4x = 4(20${}^{\circ }$) = 80${}^{\circ }$

The difference between the largest and the smallest angle is 80${}^{\circ }$ - 40${}^{\circ }$ = 40${}^{\circ }$.