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(b) In the figrue (ii) given below, O is the centre of the circle. If ∠AOB = 140° and ∠OAC = 50°, find (i) ∠ACB (ii) ∠OBC (iii) ∠OAB (iv) ∠CBA

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This is the basic and conceptual 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 angles <ACB, <OBC, <OAB, <CBA

ICSE Avichal publication
Understanding ICSE Mathematics
Question 5 (b)

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1 Answer

  1. (b) (i)
    AOB + reflex AOB = 360o

    (Angles at the point)

    140+ reflex AOB = 360o

    Reflex AOB = 360– 140= 220o

    ML Aggarwal Solutions for Class 10 Chapter 15 - Image 10

    Now major arc AB subtends AOB OBC = 360o

    50+ 110+ 140OBC = 3600

    300+ ∠OBC = 3600

    ∠300o + ∠OBC = 3600

    ∠OBC = 360o – 300o

    ∠OBC = 60o

    (ii) In Quadrilateral .OACB

    ∠OAC + ∠ACB + ∠AOB + ∠OBC = 360o

    50+ 110+ 140o + ∠OBC = 360o

    300o + ∠OBC = 360o

    ∠OBC = 360o – 300o

    ∠OBC =60o

    (iii) in ∆OAB,

    OA = OB

    (Radii of the same circle)

    ∠OAB + ∠OBA = 180o

    2 ∠OAB = 180o – 140= 40o

    ∠OAB = 40o/2 = 200

    But ∠OBC = 60o

    ∠CBA = ∠OBC – ∠OBA

    = 60o – 20= 40o

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