\(OM\) is the angle bisector of \(\angle POQ\). \(NP\) and \(NQ\) meet \(OA\) and \(OB\) respectively at \(42^\circ\). Complete the missing fields to prove that the triangles \(OPN\) and \(OQN\) are congruent to each other.
Proof:
We know that \(OM\) is the angle bisector of \(\angle \).
Hence, \(\angle PON = \angle\).
[Since the angles mentioned in the previous step are bisected angles]
To prove that triangles \(OPN\) and \(OQN\) are congruent to each other, let us now consider \(\triangle OPN\) and \(\triangle OQN\).
\(\angle OPN = \angle OQN =\) \(^\circ\) [Given]
Also, is common to both \(\triangle OPN\) and \(\triangle OQN\).
Here, two corresponding pair of angles and one corresponding pair of sides are equal.
Therefore by congruence criterion, \(\triangle OPN \cong \triangle OQN\).