Question

2
In fig. 10.6, if angle OAB = 40,
then angle ACB is equal to:
(i) 40 degree (ii) 60 degree
(iii) 50 degree (iv) 70 degree
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Answer 1

Answer:

hello

Step-by-step explanation:

In ΔQAB, OA = OB [both are the radius of a circle]

∠OAB = ∠OBA ⇒ ∠OBA = 40°

[angles opposite to equal sides are equal] Also, ∠AOB + ∠OBA + ∠BAO = 180°

[by angle sum property of a triangle]

∠AOB + 40° + 40° = 180°

⇒ ∠AOB = 180° – 80° = 100°

We know that, in a circle, the angle subtended by an arc at the centre is twice the angle subtended by it at the remaining part of the circle.

∠AOB = 2 ∠ACB ⇒ 100° =2 ∠ACB

∠ACB = 100°/2 = 50°

hope it helped you!