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If O is the centre of the circle, find the value of x in each of the following figures (using the given information):

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

ICSEIn this question we have figure of circles with constructions and we have to find the value of x using basic properties of circles.

Avichal publication
Understanding ICSE Mathematics


1 Answer

  1. Arc AB subtends ∠AOD at the centre and ∠ACD at the remaining part of the Circle

    ∠AOD = 2 ∠ACB

    ∠ACB = ½ ∠AOD = ½ × 70= 35o

    ∠CMO = 90o

    ∠AMC = 90o

    (∠AMC + ∠CMO = 180o)

    ML Aggarwal Solutions for Class 10 Chapter 15 - Image 5

    Now in ∆ACM

    ∠ACM + ∠AMC + ∠CAM = 180o

    35o + 90+ x= 180o

    125+ x= 180o

    X= 180 – 125= 55o

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