Question

Draw an angle of ${80}^{\circ }$ with the help of protractor. Then, construct angles of
(i) ${40}^{\circ }$
(ii) ${160}^{\circ }$
(iii) ${120}^{\circ }$

Answer 1

First, draw an angle of ${80}^{\circ }$ say $\angle QOA={80}^{\circ }$ with the help of protractor. Now, use the following steps to construct angles of
(i) ${40}^{\circ }$
(ii) ${160}^{\circ }$
(iii) ${120}^{\circ }$

(i) Taking O as the centre and any radius draw an arc which intersects OA at E and OQ at F.

(ii) Taking E and F as the centres and radius more than $\frac{1}{2}$ EF draw arcs which intersect each other at P.

(iii) Join OP, thus, $\angle POA={40}^{\circ }[\because {40}^{\circ }=\frac{1}{2}\times {80}^{\circ }]$

(iv) Now, taking F as the centre and radius equal to EF draw an arc which intersects the arc drawn in step (i) at S.

(v) Join OS, thus, $\angle SOA={160}^{\circ }$

(vi) Taking S and F as centre and radius more than $\frac{1}{2}SF$ draw arcs which intersect each other at R.(Or simply we need to bisect $\angle SOF={80}^{\circ }$)

(vii) Join OR, thus,
$\angle ROA=\angle ROQ+\angle QOA={40}^{\circ }+{80}^{\circ }={120}^{\circ }$