Question

In Figure, if angle ABC = 20°, then find angle AOC.
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Answer 1

Answer:

Step-by-step explanation:

Given, ∠ABC = 20°

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

∠AOC = 2∠ABC = 2 x 20° = 40°

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Answer 2

Answer:

If ∠ABC = 20⁰, then ∠AOC = 40⁰ .

Step-by-step explanation:

• Inscribed Angle Theorem states that, "An angle inscribed in a circle at its circumference is equal to half of the angle at centre that subtends the same arc on the circle."

Given that :

• ∠ABC = 20⁰

To find :

• ∠AOC

Solution:

• Let, ∠AOC = x⁰ .
• ∠ABC is the angle subtended at the circumference and ∠AOC is the angle at centre through the same arc.
• According to Inscribed angle theorem, ∠AOC = 2∠ABC
• ∠AOC = 2 x (20⁰) .
• ∠AOC = 40⁰.
• Hence, ∠AOC = 40⁰ .