(N/A) Steps of construction:
$1$. Draw a ray $OA$.
$2$. With $O$ as the center and any convenient radius,draw an arc cutting $OA$ at point $B$.
$3$. With $B$ as the center and the same radius,draw an arc cutting the previous arc at point $C$. This represents $60^{\circ}$.
$4$. With $C$ as the center and the same radius,draw an arc cutting the first arc at point $D$. This represents $120^{\circ}$.
$5$. With $D$ as the center and the same radius,draw an arc further along the circle to point $E$. This represents $180^{\circ}$.
$6$. Bisect the angle between $120^{\circ}$ (point $D$) and $180^{\circ}$ (point $E$) to get $150^{\circ}$. Let this point be $F$.
$7$. Now,bisect the angle between $120^{\circ}$ (point $D$) and $150^{\circ}$ (point $F$) to get $135^{\circ}$.
$8$. Draw a ray $OG$ passing through this point. The angle $\angle AOG = 135^{\circ}$.