Question

The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. Find the measure of each angle.

Answer 1

Let the angles be $\left(x\right)°,\left(2x\right)°,\left(3x\right)°\mathrm{and}\left(4x\right)°.$
Sum of the angles of a quadrilateral is ${360}^{\circ }$.
$$\begin{gathered} x+2x+3x+4x=360 \\ 10x=360 \\ x=\frac{360}{10} \\ x=36 \end{gathered}$$

$$\begin{gathered} \left(2x\right)°=(2\times 36{)}^{\circ }={72}^{\circ } \\ (3x)°=(3\times 36{)}^{\circ }={108}^{\circ } \\ \left(4x\right)°=(4\times 36{)}^{\circ }={144}^{\circ } \end{gathered}$$

The angles of the quadrilateral are ${36}^{\circ },{72}^{\circ },{108}^{\circ }\mathrm{and}{144}^{\circ }.$