Question

Draw an angle of measure ${45}^{\circ }$ and bisect it.

Answer 1

The bisector of an angle (also called angle bisector) is a ray whose end point is the vertex of the angle and which divides the angle into two equal angles

Steps of construction:
(a) Draw a line PQ and take a point O on it.
(b) Taking O as centre and a convenient radius, draw an arc which intersects PQ at two points A and B.
(c) Taking A and B as centres and radius more than half of AB, draw two arcs which intersect each other at C.
(d) Join OC. Then $\angle COQ$ is an angle of ${90}^{\circ }$
(e) Draw $\overline{OE}$ as the bisector of $\angle COE.$ Thus, $\angle QOE={45}^{\circ }$
(f) Again draw $\overline{OG}$ as the bisector of $\angle QOE.$ Thus,$\angle QOG=\angle EOG=22{\frac{1}{2}}^{\circ }$