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Question

If O is the centre of the given circle, such that ∠AOC = 110° and side AB is produced to D, find ∠CBD.

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Solution

MajorAOC=360°-110°=250° (complete angle)We know that the angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.So,CBA=12MajorAOCCBA=12×250°CBA=125°Now,CBA+CBD=180° (Linear pair)CBD=180°-CBA CBA=180°-125°CBA=55°

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