Question

In the adjoining figure, m (arc NS) = 125° , m(arc EF) = 37° , find the measure of ∠NMS.

Answer 1

Chords EN and FS intersect externally at point M. 

m∠NMS = 1/2 [m (arc NS) – m(arc EF)] 

= 1/2 (125° – 37°) = 1/2 × 88° 

∴ m∠NMS = 44°