A line passing through M intersects the first circle again at point A and the second circle again at point B. Another line passing through N intersects the first circle again at point C and the second circle again at point D. If ∠ANC = 50° and ∠BMD = 60°, what is the value of ∠AMN + ∠BNM?
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Correct answer: C
Explanation
In the first circle –
∠ANC = 50°
Angles subtended by the same arc AC are equal.
∠AMC = 50°
MA and MB lie on the same straight line at M.
∠CMN = 180° − 50° = 130°
In the second circle –
∠BMD = 60°
Angles subtended by the same arc BD are equal.
∠BND = 60°
C, N, and D lie on the same line.
∠BNM = 180° − 60° = 120°
∠AMN + ∠BNM = 50° + 60° = 110°