In the above figure O is the center of the circle and ∠AOB = 80∘, then match the following.
AngleValue1. ACB a. 902. ADBb. 403. ABCc. 804. AOCd. 180
a-4, b-3, c-2, d-1
AOC is a straight line, so ∠AOC should be a straight angle. Therefore ∠AOC= 180∘.
Diameter is also a chord of the circle. The angle subtended by AC at the center is ∠AOC = 180∘.
Since the angle subtended by a chord at the center is equal to twice the angle subtended by it at any other point on the circle.
We get ∠AOC = 2 ∠ABC
∠ABC = 90∘
Similarly, ∠ADB = 12 ∠AOB
∠ACB= 12 ∠AOB
From the above, we can see that ∠ADB = ∠ACB = 12 ∠AOB
∠ADB = ∠ACB = 40∘