ABCD is a cyclic quadrilateral such that ∠ADB = 30° and ∠DCA = 80°, then ∠DAB =

(a) 70°

(b) 100°

(c) 125°

(d) 150°

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Solution

(a) 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°

Hence the correct answer is option (a).

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