Question

In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1 : 2 : 4 : 5. Find the measure of each angle of the quadrilateral.

Answer 1

$$\begin{gathered} \mathrm{Let}x\mathrm{be}\mathrm{the}\mathrm{measure}\mathrm{of}\mathrm{each}\mathrm{angle}. \\ \mathrm{Then}\mathrm{the}\mathrm{ratio}\mathrm{becomes}x:2x:4x:5x. \\ \mathrm{Since},\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{all}\mathrm{angles}\mathrm{in}\mathrm{a}\mathrm{quadrilateral}\mathrm{is}360°,\mathrm{we}\mathrm{have}: \\ x+2x+4x+5x=360° \\ \Rightarrow 12x=360° \\ \Rightarrow x=\frac{360°}{12} \\ \Rightarrow x=30° \\ \mathrm{Thus},\mathrm{the}\mathrm{angles}\mathrm{are}: \\ x=30° \\ 2x=60° \\ 4x=120° \\ 5x=150° \end{gathered}$$