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In the figure (ii) given below, it is given that O is the centre of the circle and ∠AOC = 130°. Find∠ABC

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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 been given figure of circle with certain information about the figure and we have to find the value of angle ABC using the properties of circles.

ICSE Avichal publication
Understanding ICSE Mathematics
Question no 3(b)


1 Answer

  1. (b) ∠AOC + reflex ∠AOC = 360o

    130+ Reflex ∠AOC = 360o

    ∠AOC = 360– 130= 230o

    Now arc BC Subtends reflex ∠AOC at the centre and ∠ ABC at the remaining part of the circle.

    Reflex ∠AOC = 2 ∠ABC

    ∠ABC =1/2 reflex ∠AOC

    = ½ × 230= 115o

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