Question

The angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9. Find the measure of each of these angles.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{measures}\mathrm{of}\mathrm{the}\mathrm{angles}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{quadrilateral}\mathrm{be}\left(3x\right)°,\left(5x\right)°,\left(7x\right)°\mathrm{and}\left(9x\right)°. \\ \mathrm{Sum}\mathrm{of}\mathrm{all}\mathrm{the}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{quadrilateral}\mathrm{is}{360}^{\mathrm{o}}. \\ \therefore 3x+5x+7x+9x=360 \\ 24x=360 \\ x=15 \end{gathered}$$
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$$\begin{gathered} \mathrm{Angles}\mathrm{measure}: \\ (3\times 15)°={45}^{°} \\ (5\times 15)°={75}^{°} \\ (7\times 15)°={105}^{°} \\ (9\times 15)°={135}^{°} \end{gathered}$$