Asked in: March 2024, July 2025 and June 2026 board papers In the following figure, m(arc NS) = 125^°, m(arc EF) = 37^°. Find the measure of ∠ NMS. [Figure: chords EN and FS of a circle, extended, intersect at point M outside the circle; arc EF is the near arc and arc NS the far arc.]

Answer: m∠ NMS = 44^° Chords EN and FS intersect at M in the exterior of the circle. m∠ NMS = 1/2[m(arc NS) - m(arc EF)] ...... (theorem of angle between two chords intersecting outside the circle) = 1/2[125^° - 37^°] = 1/2 × 88^° = 44^°.

Chapter: Circle· Mathematics Part 2 (Geometry)

Asked in: March 2024, July 2025 and June 2026 board papersIn the following figure, \(m(\text{arc } NS) = 125^\circ\), \(m(\text{arc } EF) = 37^\circ\). Find the measure of \(\angle NMS\).[Figure: chords EN and FS of a circle, extended, intersect at p…

Asked in: March 2024, July 2025 and June 2026 board papers

In the following figure, \(m(\text{arc } NS) = 125^\circ\), \(m(\text{arc } EF) = 37^\circ\). Find the measure of \(\angle NMS\).

[Figure: chords EN and FS of a circle, extended, intersect at point M outside the circle; arc EF is the near arc and arc NS the far arc.]

Doubtly Asked 29 Oct 2026 Practice test ssc 10th Save WhatsApp Report

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Answer: \(m\angle NMS = 44^\circ\)

Chords EN and FS intersect at M in the exterior of the circle.

\(m\angle NMS = \dfrac{1}{2}\left[m(\text{arc } NS) - m(\text{arc } EF)\right]\) ...... (theorem of angle between two chords intersecting outside the circle)

\(= \dfrac{1}{2}\left[125^\circ - 37^\circ\right] = \dfrac{1}{2} \times 88^\circ = 44^\circ\).

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

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Asked in: March 2024, July 2025 and June 2026 board papersIn the following figure, \(m(\text{arc } NS) = 125^\circ\), \(m(\text{arc } EF) = 37^\circ\). Find the measure of \(\angle NMS\).[Figure: chords EN and FS of a circle, extended, intersect at p…

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