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(a)
radii of semi-circle, OP = OQ = OR = MR (given)
angle NOR = angle RMN = 21 (isos. triangle)
angle ORQ = 21 + 21 = 42 (ext. angle = 2 int. opp angles)

(b)
angle QOR = 180 – 42 – 42 = 96 (isos. triangle)
angle POQ = 180 – 96 – 21 = 63 (sum of angles on a triangle)
angle OPQ = (180 – 63)/2 = 58.5 (isos. triangle)

Ans : (a) 42 degrees; (b) 58.5 degrees.

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