Question

Draw an angle of 60°, using a pair of compasses. Bisect it to make an angle of 30°.

Answer 1

Constructions steps:

1. Draw a ray QP.
2. Wth Q as the centre and any convenient radius,draw an arc cutting QP at N.
3. With N as the centre and radius same as before, draw another arc to cut the previous arc at M.
4. Draw QM and produce it to R.
$\angle \mathrm{PQR}\mathrm{is}\mathrm{an}\mathrm{a}\mathrm{ngle}\mathrm{of}60°.$
5. With M as the centre and radius more than half of MN, draw an arc.
6. With N as the centre and radius same as in step (5), draw another arc, cutting the previously drawn arc at point X.
7. Draw QX and produce it to point S.
Ray QS is the bisector of $\angle PQR$.