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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, - Mathematics

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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,  

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)

  Is there an error in this question or solution?
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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 17: Circles
Exercise 17(A) | Q: 25.1 | Page no. 259
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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, Concept: Arc and Chord Properties - Angle in a Semi-circle is a Right Angle.
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