Question

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Answer 1

Hey!!!!!

Here is an attachment.

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Answer 2

[✖‿✖]

given :-

O is the center of the circle.

angle OAB = 30° and angle OCB = 57°

in ∆OAB,

⏩ OA = OB (radii of the circle)

therefore angle OAB = angle OBA (angles opposite to opposite sides are equal)

angle OBA = 30°

similarly, angle OBC = 57° (since OB and OC are radii i.e equal and angles opposite to opposite sides are equal)

now,

angle BOC + angle OCB + angle OBC = 180° (angle sum property)

⏩ angle BOC + 57° + 57° = 180°

⏩ angle BOC + 114° = 180°

⏩ angle BOC = 180° - 114°

⏩ angle BOC = 66°

similarly,

angle OAB + angle AOB + angle OBA = 180°

⏩ 30° + angle AOB + 30° = 180°

⏩ 60° + angle AOB = 180°

⏩ angle AOB = 180° - 60°

⏩ angle AOB = 120°

angle AOC + angle BOC = angle AOB

⏩ angle AOC + 66° = 120°

⏩ angle AOC = 120° - 66°

⏩ angle AOC = 54°