Question

The angles of a quadrilateral are in the ratio 2 : 3 : 5 : 8. Find all the angles of the quadrilateral.

Answer 1

The measures of the angles of the quadrilateral are in the ratio 2:3:5:8.
Now, let the measures of the angles be 2x, 3x, 5x and 8x.
Also, we know that the sum of all angles of a quadrilateral is 360^o.
Thus, we have:
$$\begin{gathered} 2x+3x+5x+8x=360° \\ \Rightarrow 18x=360° \\ \Rightarrow x=\frac{360}{18} \\ \Rightarrow x=20° \end{gathered}$$

Thus, the measures of the angles are:
$$\begin{gathered} 2x=2\times 20°=40° \\ 3x=3\times 20°=60° \\ 5x=5\times 20°=100° \\ 8x=8\times 20°=160° \end{gathered}$$
$\therefore \mathrm{The}\mathrm{measures}\mathrm{of}\mathrm{the}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{quadrilateral}\mathrm{are}40°,60°,100°\mathrm{and}160°$