#### Question

In the given figure, AB is a diameter of the circle. Chord ED is parallel to AB and ∠EAB = 63°. Calculate

(i) ∠EBA (ii) ∠BCD

#### Solution

(i) ∠AEB = 90

(Angle in a semicircle is a right angle)

Therefore ∠EBA = 90° - ∠EAB = 90° - 63° = 27°

(ii) AB || ED

Therefore ∠DEB = EBA = 27° (Alternate angles)

Therefore BCDE is a cyclic quadrilateral

Therefore ∠DEB + ∠BCD = 180°

[pair of opposite angles in a cyclic quadrilateral are supplementary]

Therefore ∠BCD =180° - 27° =153°

Is there an error in this question or solution?

Solution In the Given Figure, Ab is a Diameter of the Circle. Chord Ed is Parallel to Ab and ∠Eab = 63°. Calculate (I) ∠Eba (Ii) ∠Bcd Concept: Arc and Chord Properties - Angle in a Semi-circle is a Right Angle.