Question

In cyclic quadrilateral ABCD, ∠DAC = 27°; ∠DBA = 50° and ∠ADB = 33°.

Calculate:

1. ∠DBC,
2. ∠DCB,
3. ∠CAB.

Answer 1

i. ∠DBC = ∠DAC = 27°

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

ii. ∠ACB = ∠ADB = 33°

∠ACD = ∠ABD = 50°

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

∴ ∠DCB = ∠ACD + ∠ACB

= 50° + 33°

= 83°

iii. ∠DAB + ∠DCB = 180°

(Pair of opposite angles in a cyclic quadrilateral are supplementary)

`=>` 27° + ∠CAB + ∠83° = 180°

`=>` ∠CAB = 180° – 110° = 70°