Mathematics
In the figure (i) given below, M, A, B, N are points on a circle having center O. AN and MB cut at Y. If ∠NYB = 50° and ∠YNB = 20°, find ∠MAN and the reflex angle MON.
Answer
Considering △YBN,
Since sum of angles in a triangle is equal to 180°.
⇒ ∠NYB + ∠YNB + ∠YBN = 180°.
⇒ 50° + 20° + ∠YBN = 180°
⇒ 70° + ∠YBN = 180°
⇒ ∠YBN = 180° - 70°
⇒ ∠YBN = 110°.
From figure,
∠MBN = ∠YBN = 110°.
Considering △MAN and △MBN,
∠MAN = ∠MBN = 110° (∵ angles in same segment are equal.)
MN subtends Reflex ∠MON at center and ∠MAN at point A of circle.
⇒ Reflex ∠MON = 2 ∠MAN = 2 × 110° = 220°.
Hence, ∠MAN = 110° and Reflex ∠MON = 220°.
Related Questions
In the figure (i) given below, O is the center of the circle and ∠PBA = 42°. Calculate the value of ∠PQB.
In the figure (ii) given below, O is the center of the circle. Calculate the values of x and y.
In the figure (ii) given below, O is the center of the circle. If ∠AOB = 140° and ∠OAC = 50°, find
(i) ∠ACB
(ii) ∠OBC
(iii) ∠OAB
(iv) ∠CBA.
In the figure (i) given below, calculate the values of x and y.