91Ó°ÊÓ

The given diagram is:

As, $\stackrel{→}{OB}$bisects the angle AOC, therefore the rayOB is the angle bisector of AOC.

Therefore, by using the angle bisector theorem it can be said that the measures of the angles∠4and∠5are equal.

That implies, $m∠4=m∠5$.

Therefore, the relation between the angles ∠4 and ∠5 is $m∠4=m∠5$.

From the given diagram it can be noticed that the angles∠3,∠4and∠5lies on the same straight-line EC.

Therefore, the sum of the angles ∠3, ∠4 and ∠5 is $180°$.

That implies $m∠3+m∠4+m∠5=180°$.

Therefore, the relation between the angles ∠3, ∠4 and ∠5 is $m∠3+m∠4+m∠5=180°$.

As $m∠3+m∠4+m∠5=180°$, $m∠4=m∠5$, $m∠5=2x$and $m∠3=x$.

Therefore, the value of x is given by :

$m∠3+m∠4+m∠5=180°$

$m∠3+m∠5+m∠5=180°$

$x+2x+2x=180°$

$5x=180°$

$x=\frac{180}{5}$

$x=36$

Therefore, the value of x is 36.