Question

In the adjoining figure, x:y:z = 5:4:6. If XOY is a straight line, find the values of x, y and z.

Answer 1

Let $x=5a,y=4a\text{and}z=6a$
XOY is a straight line. Therefore,

$$\begin{gathered} \angle XOP+\angle POQ+\angle YOQ=180° \\ \Rightarrow 5a+4a+6a=180° \\ \Rightarrow 15a=180° \\ \Rightarrow a=12° \end{gathered}$$
Therefore,

$$\begin{gathered} x\Rightarrow 5\times 12°=60° \\ y\Rightarrow 4\times 12°=48° \\ \mathrm{and}z\Rightarrow 6\times 12°=72° \end{gathered}$$