Question

Draw an angle of measure ${135}^{\circ }$ and bisect it.

Answer 1

Steps of construction:
(a) Draw a line PQ and take a point O on it.
(b) Taking O as centre and convenient radius, mark an arc, which intersects PQ at A and B.
(c) Taking A and B as centres and radius more than half of AB, draw two arcs intersecting each other at R.
(d) Join OR. Thus, $\angle QOR=\angle POQ={90}^{\circ }$
(e) Draw $\overline{OD}$ the bisector of $\angle POR.$ Thus, $\angle QOD$ is the required angle of ${135}^{\circ }$
(f) Now, draw $\overline{OE}$ as the bisector of $\angle QOD.$

Thus, $\angle QOE=\angle DOE=67{\frac{1}{2}}^{\circ }$