Question

Find the angles of a triangle which are in the ratio $$5 : 4 : 3$$.

Answer 1

Let the angles of the triangle be $$5x$$, $$4x$$ and $$3x$$.

The sum of the angles of a triangle is $$180^\circ$$: $$5x + 4x + 3x = 180^\circ$$

$$12x = 180^\circ$$

$$\implies x = \frac{180^\circ}{12} = 15^\circ$$

The angles are:

$$5x = 5 \times 15^\circ = 75^\circ$$

$$4x = 4 \times 15^\circ = 60^\circ$$

$$3x = 3 \times 15^\circ = 45^\circ$$

Therefore, the angles are $$75^\circ$$, $$60^\circ$$ and $$45^\circ$$.