Question

Draw an arc with seg MN = 8.9 cm inscribing $\angle$MPN = 125$°$.

Answer 1

Chord MN subtends $\angle$MPN.
$\angle$MON is inscribed in arc MPN.
$\angle$MON is the centre angle.
$$\begin{gathered} \angle \mathrm{MPN}=125° \\ \angle \mathrm{MON}=250° \\ \mathrm{reflex}\angle \mathrm{MON}=360°-270°=110° \\ \therefore \angle \mathrm{NMO}=\angle \mathrm{MNO}=35° \end{gathered}$$

Steps of construction:
1. Draw a segment MN =8.9 cm.
2. Draw rays MX and NY making an angle of 35$°$ on the same side. O is the intersection point of these rays.
3. Draw an arc with centre O and radius OM or ON on the centre side.
4. Take a point P on the arc. Join PM and PN.
Thus, arc MPN is the required arc.