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:

1. ∠DAB,
2. ∠BDC.

ABCD is a cyclic quadrilateral and DC || AB. If AB is the diameter of the circle and BED = 65°, find:

1. ∠DAB
2. ∠BDC

Answer 1

(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°.