The diagonals of a rhombus, ABCD intersect at the point O. If ∠BDC = 50°, then ∠OAB = ?

Question

The diagonals of a rhombus, ABCD intersect at the point O. If ∠ BDC = 50°, then ∠ OAB = ?

Philoid · Accepted Answer

∠BDC = ∠ABD (Alternate interior angles)

∠ABD = 50^o

Now, In ∆AOB,

∠DBA = 50^o and ∠AOB = 90^o

Thus, ∠OAB = 180^o − (90^o + 50^o)

∠OAB = 180° - 140°

∠OAB = 40^o

∴ Option B is correct.