Question

If the angles of a quadrilateral are in the ratio $2:3:4:6$, find the angles.

Answer 1

Find the angles of the quadrilateral

We know the sum of angles of a quadrilateral is $360°$

Given that the ratio of the angle is $2:3:4:6$,

Let the first angle be $2x$, second angle is $3x$ , third angle is $4x$ and the fourth angle is $6x$

So,

$$\begin{gathered} 2x+3x+4x+6x=360 \\ \Rightarrow 15x=360 \\ \Rightarrow x=24 \end{gathered}$$

Therefore

The first angle is $2x$$=48°$

The second angle is $3x=72°$

The third angle is $4x=96°$

The fourth angle is $6x=144°$

Hence, the angles are $48°,72°,96°$ and $144°$.