Question

In the below figure $AB,CD$ and $EF$ are three lines concurrent at $O$. Find the value of $y$.

Answer 1

Step 1: Calculate $\angle EOA$

From the figure, it is given that $AB,CD$ and $EF$ are three lines concurrent at $O$.

Given that $\angle BOF=5y$

So $\angle EOA=5y$ [$\because$they are vertically opposite angles]

Step 2: Calculate $y$

Again, $\angle COE+\angle EOA+\angle AOD=180°$ [$\because$sum of angles on a straight line$=180°$]

$\Rightarrow$ $2y+5y+2y=180°$

$\Rightarrow$ $9y=180°$

$\Rightarrow$ $y=\frac{180°}{9}$

$\Rightarrow$ $y=20°$

Hence the value of $y$ is $20°$.