Question

ABCD is a cyclic quadrilateral in   ∠BCD = 100° and ∠ABD = 70° find ∠ADB.

Answer 1

It is given that, ∠BCD = 100° and ∠ABD = 70°

As we know that sum of the opposite pair of angles of cyclic quadrilateral is 180°. 

\[\angle ADC + \angle ABC = 180° \]
\[ \Rightarrow 180° - 80° + 180° - x = 180°\]
\[ \Rightarrow x = 100°\]

In ΔABD we have,

\[\angle DAB + \angle ABD + \angle BDA = 180° \]
\[ \Rightarrow \angle BDA = 180° - 150° = 30° \]

_{Hence,  `angle ABD = 30°`}