Question

In a cyclic quadrilateral ABCD, m∠CAB=45 and m∠ABC=100, then m∠ADB = ______ .
(a) 55
(b) 105
(c) 80
(d) 35

Answer 1

Answer:

∠ ADB = 35°

Step-by-step explanation:

We have given a cyclic quadrilateral,

m∠CAB=45° and m∠ABC=100°

We have to find m∠ADB

Make a circle. Draw a cyclic quadrilateral and name it ABCD than Join AC and BD.

In ∠ABC

m∠CAB=45° and m∠ABC=100°

By angle sum property,

∠CAB + ∠ACB + ∠ABC = 180°

45° + ∠ACB + 100° = 180°

∠ACB = 180° - 145° = 35°

∠ACB = 35°

We get angle ∠ACB = 35°

∠ACB =  ∠ADB,

(As the are angles subtended by the same chord on the same side of the chord)

Therefore, ∠ADB = 35°