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Using the given information, find the value of x in each of the following figures

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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 ques we have been given the figure of circle and we have to find the value of x

ICSE Avichal publication
Understanding ICSE Mathematics
Question 1


1 Answer

  1. Given ∠CPB = 120o , ∠ACP = 70o

    To find, xi,e., ∠PBD

    Reflex ∠CPB = ∠BPO + ∠CPA

    120= ∠BPD + ∠BPD

    (BPD = CPA are vertically opposite ∠s)

    2∠BPD = 120o ∠PBD = 1200/2 = 60o

    Also ∠ACP and PBD are in the same segment

    ∠PBD + ∠ACP = 700

    Now, In ∆PBD

    ∠PBD + ∠PDB + ∠BPD = 180o

    (sum of all ∠s in a triangle)

    70+ xo + 600 = 180o

    x = 180– 130o

    x = 50o

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