Q29 of 141 Page 447

In the given figure, O is the centre of a circle and ∠AOC = 130°. Then, ∠ABC = ?

Given: ∠AOC = 130°


Here,


(Exterior ∠AOC) = 360° – (interior ∠AOC)


(Exterior ∠AOC) = 360° – 130°


(Exterior ∠AOC) = 230°


We know that,


(Exterior ∠AOC) = 2 × ∠ABC


230° = 2 × ∠ABC


∠ABC = = 115°


∴ ∠ABC = 115°

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