[Figure: a circle; two secants from an external point M cut the circle at E, N and at F, S respectively, so that M – E – N and M – F – S.]In the above figure, m(arc NS) = 125º, m(arc EF) = 37º. Find the measure of ∠NMS.

Q.2 (B)(3)

[Figure: a circle; two secants from an external point M cut the circle at E, N and at F, S respectively, so that M – E – N and M – F – S.]

In the above figure, m(arc NS) = 125º, m(arc EF) = 37º. Find the measure of ∠NMS.

Doubtly Asked 25 Oct 2026 ssc 10th Save WhatsApp Report

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Answer: m∠NMS = 44º

The angle between two secants drawn from an external point is half the difference of the measures of the intercepted arcs:

\(\angle NMS = \dfrac{1}{2}\left[m(\text{arc } NS) - m(\text{arc } EF)\right] = \dfrac{1}{2}(125^\circ - 37^\circ) = \dfrac{1}{2} \times 88^\circ = 44^\circ\).

Doubtly AI · 25 Oct 2026 AI-verified · Oct 2026 Report

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[Figure: a circle; two secants from an external point M cut the circle at E, N and at F, S respectively, so that M – E – N and M – F – S.]In the above figure, m(arc NS) = 125º, m(arc EF) = 37º. Find the measure of ∠NMS.

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