45°
Steps of construction :
i) Draw any ray \(\overline{OP}\) of any length.
ii) Draw arcs with the same radius from A to B and from B to C which cuts the previous arc at B and C respectively.
iii) Draw arcs from B and from C with same radius which can intersect at X.
iv) Join \(\overset\longrightarrow{OX}\) \((\overset\longrightarrow {OD})\) i.e., ∠POD = 90°.
v) Draw the bisector to ZPOD which is \(\overset\longrightarrow{OQ}\)
vi) Now, ∠POQ = ∠QOD = \(\frac{\angle POD}{2}=\frac{90}{2}\) = 45°
∴ ∠POQ = 45° (Q.E.D)
