In the given figure angle OAB = 40° .find angle ACB
Answers
∠ACB = 50° , if In the given figure angle OAB = 40°
Step-by-step explanation:
OA = OB = Radius
=> ∠OAB = ∠OBA = 40°
in Δ OAB
∠AOB + ∠OAB + ∠OBA = 180°
=> ∠AOB + 40° + 40° = 180°
=> ∠AOB = 100°
∠ACB = (1/2)∠AOB ( angle subtended by chord AB at center & arc segment)
=> ∠ACB = (1/2)100°
=> ∠ACB = 50°
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Answer:
In △OAB,
OA = OB [radii of same circle]
∠OBA = ∠OAB = 40° [∠s opp. to equal sides in a △ are equal]
Now, ∠OAB + ∠AOB + ∠OBA = 180° [angle sum properly of a △]
⇒ 40° + ∠AOB + 40° = 180°
⇒ ∠AOB = 100°
Therefore, ∠ACB = 50° [∵ angle subtended by an arc at the centre is double the angle subtended by it at the remaining part of the circle]