急!急! F4 Properties Circles q3

18) ∠DAO = ∠CDA (Alt. ∠s, CD//AB)

∠AOC = 2 ∠CDA = 52 (∠ at centre = 2 x ∠ at circum)

∠DEO = ∠AOC + ∠DAO = 78 (Ext. ∠ of triangle)

24) ∠DAB = 180 - ∠DCB = 80 (Opp. ∠s, cyclic quad)

x = 180 - ∠DAB - ∠ABD = 30

25) ∠RQO = ∠QRO = 50 (Base ∠s, isos. triangle)

∠ROQ = 180 - 50 - 50 = 100

Hence reflex ∠POR = 180 + 80 = 260

x = (1/2) x reflex ∠POR = 130 (∠ at centre = 2 x ∠ at circum)

∠PRQ = 90 (∠ in semi circle)

∠PRO = 40

∠SPR = ∠PRO = 40 (Alt. ∠s, PS//OR)

y = 180 - x - 40 = 10