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Question
MABN are points on a drde having centre O. AN and MB cut at Y. If ∠ NYB = 50" and ∠ YNB = 200, find ∠ MAN and reflex angle MON.
Solution
∠ NYB =50 °
∠ YNB = 20°
In Δ NYB,
20° + ∠ NBY + 50 ° = 180°
⇒ ∠ NBY = 180° - 70 ° = 110 °
Now, ∠ MAN = ∠ NBM = 110° (Angles in the same segment)
∠ MON = 2 ∠ MAN (Arc MN subtends ∠ MON at centre and ∠ MAN at remaining part of the circle)
∠ MON = 2(110°) = 220°
Reflex ∠ MON = 360° - ∠ MON
= 360° - 220°
Reflex ∠ MON = 140°.
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