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Question
ABCD is a cyclic quadrilateral such that ∠ADB = 30° and ∠DCA = 80°, then ∠DAB =
Options
70°
100°
125°
150°
Solution
70°
It is given that ABCD is cyclic quadrilateral ∠ADB = 90° and ∠DCA = 80°. We have to find ∠DAB
We have the following figure regarding the given information
∠BDA = ∠BCA = 30° (Angle in the same segment are equal)
Now, since ABCD is a cyclic quadrilateral
So, ∠DAB + ∠BCD = 180°
`angleDAB + angleBCA + angleDCA` = 180°
`angleDAB ` + 30° + 80° = 180°
`angleDAB` = 180° - 110°
`angleDAB ` = 70 °
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