In the following figure, chord EN and chord FS intersect each other at point M in the exterior of the circle. If \(m(\text{arc } NS) = 125^\circ\), \(m(\text{arc } EF) = 37^\circ\), then complete the following activity to find \(\angle NMS\).[Figure:…

Q.2 (A)(i) In the following figure, chord EN and chord FS intersect each other at point M in the exterior of the circle. If \(m(\text{arc } NS) = 125^\circ\), \(m(\text{arc } EF) = 37^\circ\), then complete the following activity to find \(\angle NMS\).

[Figure: M is a point outside the circle; one secant from M cuts the circle at E and then N (M – E – N) and the other cuts it at F and then S (M – F – S); both secants are extended with arrows beyond N and S.]

Activity : Chord EN and chord FS intersect each other at point M in the exterior of the circle.

\(m\angle NMS = \dfrac{1}{2}\left[\text{____} - m(\text{arc } EF)\right]\)
= \(\dfrac{1}{2}\left[\text{____} - 37\right]\)
= \(\dfrac{1}{2} \times \text{____}\)
\(\therefore m\angle NMS = \text{____}\)