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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 - ICSE Class 10 - Mathematics

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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)

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Solution 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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