Question

Date
Page
In the figure, 'O' is the center and
LOAB= 50° , then find
LACB.
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Answer 1

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 = 50⁰

By substituting

∠AOB = 2 × 50⁰

By multiplication

∠AOB = 100⁰ …… (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 = 180⁰

Using equations

(1) and (2) we get 100⁰ + 2 ∠OAB = 180o

By subtraction

2 ∠OAB = 180⁰ – 100⁰

So we get

2 ∠OAB = 80⁰

By division

∠OAB = 40⁰