# The angles of a triangle are in the ratio 2 : 3 : 4. Find the angles.

Question:

The angles of a triangle are in the ratio 2 : 3 : 4. Find the angles.

Solution:

Let the angles of the given triangle measure $(2 x)^{\circ},(3 x)^{\circ}$ and $(4 x)^{\circ}$, respectively.

Then,

$2 x+3 x+4 x=180^{\circ} \quad$ [Sum of the angles of a triangle]

$\Rightarrow 9 x=180^{\circ}$

$\Rightarrow x=20^{\circ}$

Hence, the measures of the angles are $2 \times 20^{\circ}=40^{\circ}, 3 \times 20^{\circ}=60^{\circ}$ and $4 \times 20^{\circ}=80^{\circ}$.