The diagonals of a parallelogram ABCD intersect ay O. If ∠BOC =90° and ∠BDC=50°, then ∠OAB =
Given,
ABCD is a parallelogram
Diagonals of parallelogram intersects at O
∠BOC = 90° , ∠BDC = 50°
∵ ∠BOC+∠AOB = 180° [Linear pair of angles]
90°+∠AOB = 180°
=∠AOB = 180°-90° = 90°
∠BDC = ∠OBA = 50° [Alternate angles]
In ∆AOB
∠AOB+∠OBA+∠OAB = 180°
= 90°+50°+∠OAB = 180°
= ∠OAB = 180°-140° = 40°