13 Find the value of x in the following figures, where 'O' is the centre of the circle.
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Step-by-step explanation:
(i) ∠AOC = 135° Therefore, ∠AOC + ∠BOC = 180° (Linear pair) 135° + ∠BOC = 180° ∠BOC = 45° By degree measure theorem, ∠BOC = 2∠COB 45° = 2x x = 22 1 2 12° (ii) We have, ∠ABC = 40° ∠ACB = 90° (Angle in semi-circle) In triangle ABC, By angle sum property, ∠CAB + ∠ACB + ∠ABC = 180° ∠CAB + 90° + 40° = 180° ∠CAB = 50° Now, ∠COB = ∠CAB (Angle on same segment) x = 50°
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