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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 circle based question from Chapter name- circles
Topic – Angle properties of circles
Chapter number- 15

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

ICSE Avichal publication
Understanding ICSE Mathematics
Question no 2


1 Answer

  1. ∠AOB + ∠AOC + ∠BOC = 360o

    (sum of angles at a point)

    ∠AOB + 80o + 130= 360o

    ∠AOB + 210= 360o

    ∠AOB = 360o – 210o = 1500

    Now arc AB subtends ∠AOB at the centre ∠ACB at the remaining part of the circle

    ∠AOB = 2 ∠ACB

    ∠ACB = ½ ∠AOB = ½ × 150o = 75o

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