急! F4 Properties Circles 12q2

13a) ∠KMH = 65 (∠ in the same segment)

Hence ∠KML = 65, so ∠KHN = 65 (Ext. ∠, cyclic quad)

b) △KNH is isos. △ since ∠KNH = ∠KHN

16) Let ∠BAF = x, then ∠BDF = 180 - x (Opp. ∠s, cyclic. quad)

Also ∠CDE = ∠BDF = 180 - x, hence

∠ACF + ∠AEB + ∠BAF = ∠BDF

x + 46 + 38 = 180 - x

2x = 96

x = 48

19a) Reflex ∠AOC = 2 x 130 = 260 (∠ at centre = 2 x ∠ at circum)

∠AOC = 360 - 260 = 100

b) ∠CKB = 180 - ∠AOC = 80 (Opp. ∠s, cyclic. quad)