Answer : (c) 63º
The required angle is ∠BDE. C is north of D and E is west of D
⇒ ∠CDE = 90° ⇒ EC is the diameter of the circle
(∵ Angle in a semicircle is a rt. ∠)
∴ ∠EBC = 90° (Angle in a semicircle)
∠BEC = ∠BAC = 27° (Angle in the same segment are equal)
∴ In ∆ EBC, ∠ECB = 180° – (∠EBC + ∠BEC)
= 180° – (90° + 27°) = 63°. (Angle sum property of a ∆)
⇒ ∠BDE = ∠BCE = 63° (Angles in the same segment are equal)