Solution

(a) ∠NYB = 50°, ∠YNB = 20°.

In
∆YNB,

∠NYB + ∠YNB + ∠YBN = 180o

50^o + 20^o + ∠YBN = 180^o

∠YBN + 70^o = 180^o

∠YBN = 180^o – 70^o = 110^o

But ∠MAN = ∠YBN

(Angles in the same segment)

∠MAN = 110^o

Major arc MN subtend reflex ∠MON at the

Centre and ∠MAN at the remaining part of

the choice.

Reflex ∠MAN at the remaining part of the circle

Reflex ∠MON = 2 ∠MAN = 2 × 110^o =220^o

(b) (i)
∠AOB + reflex ∠AOB = 360^o

(Angles at the point)

140^o + reflex ∠AOB = 360^o

Reflex ∠AOB = 360^o – 140^o = 220^o

Now major arc AB subtends ∠AOB + ∠OBC = 360^o

50^o + 110^o + 140^o + ∠OBC = 360⁰

300^o + ∠OBC = 360⁰

∠300^o + ∠OBC = 360⁰

∠OBC = 360^o – 300^o

∠OBC = 60^o

(ii) In Quadrilateral .OACB

∠OAC + ∠ACB + ∠AOB + ∠OBC = 360^o

50^o + 110^o + 140^o + ∠OBC = 360^o

300^o + ∠OBC = 360^o

∠OBC = 360^o – 300^o

∠OBC =60^o

(iii) in ∆OAB,

OA = OB

(Radii of the same circle)

∠OAB + ∠OBA = 180^o

2 ∠OAB = 180^o – 140^o = 40^o

∠OAB = 40^o/2 = 20⁰

But ∠OBC = 60^o

∠CBA = ∠OBC – ∠OBA

= 60^o – 20^o = 40^o