Question

The diagonals of a parallelogram ABCD intersect ay O. If ∠BOC = 90° and ∠BDC = 50°, then ∠OAB = 

A. 40° 

B. 50° 

C. 10° 

D. 90°

Answer 1

Option : (A)

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°