Question

Construct an arc DCV, such that seg DV of length 9.5 cm, subtends an angle of 135$°$ on it.

Answer 1

Chord DV subtends an angle $\angle$DCV.

$$\begin{gathered} \angle \mathrm{DCV}=135° \\ \mathrm{major}\angle D\mathrm{O}V=270° \\ \mathrm{minor}\angle \mathrm{DOV}=360°-270°=90° \\ \therefore \angle \mathrm{VDO}=\angle \mathrm{DVO}=45° \end{gathered}$$

Steps of construction:
1. Draw a segment DV = 9.5 cm.
2. Draw rays DY and VX making an angle of 45^o on the same side. O is the intersection point of these rays.
3. Draw an arc with O as the centre and OD or OV as the radius opposite to the centre side.
4. Take a point C on the arc. Join CD and CV.
Then, arc DCV is the required arc.