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

Question

The diagonals of a parallelogram ABCD intersect ay O. If &#x2220; BOC =90&#xB0; and &#x2220; BDC=50&#xB0;, then &#x2220; OAB =

Philoid · Accepted Answer

∠BOC is 90°

So,

∠COD and ∠AOB all should be 90° by linear pair

∠BDC is 50°,

So,

Now as in a parallelogram the opposite sides are equal

We say,

AB parallel to CD

∠DCA = 50°

So,

In triangle COA

∠C = 50° (Stated above)

∠COA = 90° (Proved above)

Therefore,

90° + 50° + x° = 180°

x = 40°