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.

Answer 1

∠ 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°.