Question

Using a pair of compasses construct the following angles:
(i) 60°
(ii) 120°
(iii) 90°

Answer 1

(i)
Steps for construction:
1. Draw a ray QP.
2. With Q as the centre and any convenient radius, draw an arc cutting QP at N.
3. With N as the centre and the same radius as before, draw another arc to cut the previous arc at M.
4. Draw QM and produce it to R.
^$\angle$ PQR is the required angle of 60^o.
(ii)
Steps for construction:
1. Draw a ray QP.
2. With Q as the centre and any convenient radius, draw an arc cutting QP at N.
3. With N as the centre and the same radius, cut the arc at A. Again, with A as the centre and the same radius, cut the arc at M.
4. Draw QM and produce it to R.
^{$\angle \mathrm{PQR}\mathrm{is}\mathrm{the}\mathrm{required}\mathrm{angle}\mathrm{of}120°.$}

(iii)
Steps for construction:
1. Draw a line PX.
2. Take a point Q on AC. With Q as the centre and any convenient radius, draw an arc cutting AX at M and N.
3. With N as the centre and radius more than half of MN, draw an arc.
4. With M as the centre and the same radius as before, draw another arc to cut the previous arc at W.
5. Draw QW produce it to R.
$\angle \mathrm{PQR}\mathrm{is}\mathrm{required}\mathrm{angle}\mathrm{of}90°.$