#### Question

ABCD is a cyclic quadrilateral in which AB is parallel to DC and AB is a diameter of the circle. Given ∠BED = 65°; Calculate:

(i) ∠DAB, (ii) ∠BDC

#### Solution

(i) ∠DAB = ∠BED = 65°

(Angle subtended by the same chord on the circle are equal)

(ii) ∠ADB = 90°

(Angle in a semicircle is a right angle)

∴ ∠ABD = 90° - ∠DAB = 90° - 65° = 25°

AB || DC

∴ ∠BDC = ∠ABD = 25° (Alternate angles)

Is there an error in this question or solution?

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Abcd is a Cyclic Quadrilateral in Which Ab is Parallel to Dc and Ab is a Diameter of the Circle. Given ∠Bed = 65°; Calculate: (I) ∠Dab, (Ii) ∠Bdc Concept: Arc and Chord Properties - Angle in a Semi-circle is a Right Angle.

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