Q. 105.0( 3 Votes )

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

A. 50^{o}

B. 40^{o}

C. 25^{o}

D. 20^{o}

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.

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