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Question 5. (a) In the figure (i) given below, M, A, B, N are points on a circle having centre O. AN and MB cut at Y. If ∠NYB = 50° and ∠YNB = 20°, find ∠MAN and the reflex angle MON.

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This is an important and exam oriented question from Chapter name- circles
Topic – Angle properties of circles
Chapter number- 15

In this question we have been given the figure of circle with certain information about the figure and we have to find the value of angle <MAN and <MON
ICSE Avichal publication
Understanding ICSE Mathematics
Question 5(a)


1 Answer

  1. Solution

    (a) ∠NYB = 50°, ∠YNB = 20°.

    ML Aggarwal Solutions for Class 10 Chapter 15 - Image 9


    NYB + ∠YNB + YBN = 180o

    50+ 20+ ∠YBN = 180o

    YBN + 70= 180o

    YBN = 180– 70= 110o

    But MAN = YBN

    (Angles in the same segment)

    MAN = 110o

    Major arc MN subtend reflex MON at the

    Centre and MAN at the remaining part of

    the choice.

    Reflex MAN at the remaining part of the circle

    Reflex MON = 2 MAN = 2 × 110=220o

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