It is to be noted that where the above is given, the value of AD is 7 Option A.
AD/Sin ∠ABD = AB/Sin ∠ADB
DC/Sin ∠DBC = BC/ Sin ∠BDC
DC /Sin ∠ABD = BC/Sin(π-∠ADB)
2x + 4/Sin∠ABD = 12/Sin (π-∠ADB) = 12 / Sin ∠ADB
5x + 3/Sin ∠ABD = 15/Sin ∠ADB
2x + 4/ 5x + 3 = 12/15 = 4/5
20x + 12 = 10x + 20
10x = 8
x = 0.8
AD = 5x + 3
= 5 (0.8) + 3
= 4 + 3
= 7
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