Question

Construct an arc PQM such that seg PM of length 6.2 cm subtends an angle of 40$°$ on it.

Answer 1

Chord PM subtends $\angle$PQM.
$\angle$POM is the centre angle.
$$\begin{gathered} \angle \mathrm{PQM}=40° \\ \angle \mathrm{POM}=80° \\ \therefore \angle \mathrm{OPM}=\angle \mathrm{OMP}=50° \end{gathered}$$

Steps of construction:
1. Draw a segment PM = 6.2 cm.
2. Draw rays PX and MY making an angle of $50°$ on the same side. O is the intersection point of these rays.
3. Draw an arc with centre O and radius OP or OM on the centre side.
4. Take a point Q on the arc. Join QP and QM.
Thus, arc PQM is the required arc.