Mathematics
ABCD is a cyclic quadrilateral such that ∠ADB = 45° and ∠DCA = 55°, then ∠DAB is equal to :
55°
45°
100°
80°
Circles
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Answer
∠ACB = ∠ADB = 45° [Angles in the same segment]
From figure,
∠BCD = ∠ACD + ∠ACB
∠BCD = 55° + 45° = 100°
In a cyclic quadrilateral, the sum of opposite angles is 180°.
∠DAB + ∠BCD = 180°
∠DAB = 180° - ∠BCD
∠DAB = 180° - 100° = 80°.
Hence, option 4 is the correct option.
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