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In the given figure, RS is a diameter of the circle. NM is parallel to RS and ∠MRS = 29°. Calculate : ∠RNM

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Question

In the given figure, RS is a diameter of the circle. NM is parallel to RS and ∠MRS = 29°. Calculate : ∠RNM

Sum
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Solution


Join RN and MS.

∴ ∠RMS = 90°

(Angle in a semicircle is a right angle)

∴ ∠RSM = 90° – 29° = 61°

(By angle sum property of triangle RMS)

∴ ∠RNM = 180° ∠RSM = 180° – 61° = 119°

(Pair of opposite angles in a cyclic quadrilateral are supplementary)

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Chapter 17: Circles - Exercise 17 (A) [Page 259]

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Selina Concise Mathematics [English] Class 10 ICSE
Chapter 17 Circles
Exercise 17 (A) | Q 25. (i) | Page 259

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