Question

Draw an angle of ${80}^{\circ }$ with the help of protractor. Then, which of the following angles can be constructed using ${80}^{\circ }$ ?

• A. 40°
• B. 160°
• C. 110°
• D. 150°

Answer 1

Answer: (A), (B)

The correct options are
A 40°
B 160°


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) ${40}^{\circ }$
1. Taking O as the centre and any radius draw an arc which intersects OA at E and OQ at F.
2. Taking E and F as the centres and radius more than $\frac{1}{2}$ EF draw arcs which intersect each other at P.
3. Join OP, which is the angular bisector of angle QOA thus, $\angle POA={40}^{\circ }[\because {40}^{\circ }=\frac{1}{2}\times {80}^{\circ }]$

(ii) ${160}^{\circ }$
4. Now, taking F as the centre and radius equal to EF draw an arc which intersects the previous arc obtained in step1 at S.
5. Join OS,
$\angle QOA=\angle QOS={80}^{\circ }$
Thus, $\angle SOA={160}^{\circ }$