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Questions
ABCD is a cyclic quadrilateral in which AB is parallel to DC and AB is a diameter of the circle. Given ∠BED = 65°, calculate:
- ∠DAB,
- ∠BDC.
ABCD is a cyclic quadrilateral and DC || AB. If AB is the diameter of the circle and BED = 65°, find:
- ∠DAB
- ∠BDC
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Solution
(i) Find ∠DAB
Angles BED and DAB are angles subtended by the same chord DB in the same circle.
∴ ∠DAB = ∠BED = 65°
(ii) Find ∠BDC
Since AB is a diameter, angle ADB is an angle in a semicircle:
∠ADB = 90°.
In triangle ABD:
∠ABD = 180° − (∠ADB + ∠DAB)
∠ABD = 180° − (90° + 65°)
∠ABD = 25°.
AB ∥ DC,
∠ABD and ∠BDC are corresponding angles.
∴∠BDC = ∠ABD = 25°.
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