A triangle ABC is inscribed in a circle with centre O. AO is produced to meet the circle at K and AD ⊥ BC. If ∠B = 80° and ∠C = 64°, then the measure of ∠DAK is:
A. 10°
B. 16°
C. 12°
D. 20°
Answer: Option B
Solution (By Examveda Team)
∠ACK = 90° (In semicircle)
∠B = ∠K = 80°
In ΔAKC, ∠A + ∠K + ∠C = 180°
∠A + 80° + 90° = 180°
∠A = 10°
In ΔABD, ∠A = 90° - 80° = 10°
∠CAD = 90° - 64° = 26°
∠DAK = 26° - 10° = 16°
This Question Belongs to Arithmetic Ability >> Geometry
Join The Discussion