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Question

In the following figure, a circle with centre O is drawn and ∠BAC = 50°. Find x.

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Solution



As, BOC=2BAC Angle subtended by an arc at the centre is double the angle subtended by the the same arc at any point on the circleBOC=2×50°BOC=100°Now, in BOC, OB=OC Radii OBC=OCB Angles opposite to equal sides are equalOBC=OCB=xAlso,BOC+OBC+OCB=180° Angle sum property of a triangle100°+x+x=180°2x=180°-100°2x=80°x=80°2 x=40°

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