Question

ABCD is a rhombus. If ∠ACB = 40°, find ∠ADB.

 

Answer 1

\[\text{ In a rhombus, the diagonals are perpendicular } . \]
\[ \therefore \angle BPC = 90°\]
\[\text{ From ∆ BPC, the sum of angles is }180° . \]
\[ \therefore \angle CBP + \angle BPC + \angle PBC = 180°\]
\[\angle CBP = 180° - \angle BPC - \angle PBC\]
\[\angle CBP = 180° - 40° - 90° = 50° \]
\[\angle ADB = \angle CBP = 50°(\text{ alternate angle })\]