(N/A) An obtuse angle is an angle whose measure is greater than $90^{\circ}$ and less than $180^{\circ}$.
Steps of construction:
$1$. Draw a ray $OA$ using a ruler.
$2$. Place the center of the protractor at point $O$ and align the baseline with ray $OA$. Mark a point $B$ at an angle of $120^{\circ}$ (or any value between $90^{\circ}$ and $180^{\circ}$). Join $OB$.
$3$. With $O$ as the center and any convenient radius,draw an arc that intersects $OA$ at point $P$ and $OB$ at point $Q$.
$4$. With $P$ as the center and a radius more than half of $PQ$,draw an arc in the interior of the angle.
$5$. With $Q$ as the center and the same radius,draw another arc that intersects the previous arc at point $R$.
$6$. Join $OR$. The ray $OR$ is the angle bisector of $\angle AOB$.