Prove that angles in the same segment of a circle are equal

Hi!
Here is the proof of the given statement. 
Theorem: Angles is the same segment of a circle are equal
By the mentioned theorem
Reflex ∠AOB = 2∠APB and reflex ∠AOB = 2∠AQB
∴ 2∠APB = 2∠AQB
⇒ ∠APB = ∠AQB
Hence, ∠APB = ∠AQ B
 
Cheers!

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Thank you very much sir

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