Question

s in the given figure, O is the centre of the

aide IF angleACB = 50°, find angleOAB.


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Answer 1

answer :-

∠ AOB = 40°

Step-by-step explanation:

We know that the angle subtended by an arc of a circle at the centre is double the angle subtended by the arc at any point on the circumference.

So we get

∠AOB = 2 ∠ACB

It is given that ∠ACB = 50°

By substituting

∠AOB = 2 × 50°

By multiplication

∠AOB = 100° …… (1)

Consider △ OAB

We know that the radius of the circle are equal

OA = OB

Base angles of an isosceles triangle are equal

So we get

∠OAB = ∠OBA ……. (2)

Using the angle sum property

∠AOB + ∠OAB + ∠OBA = 180°

Using equations (1) and (2) we get

100° + 2 ∠OAB = 180°

By subtraction

2 ∠OAB = 180° – 100°

So we get

2 ∠OAB = 80°

By division

∠OAB = 40°

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