Question

In the given figure, ABCD is a rectangle in which diagonal AC is produced to E. If ∠ECD = 146°, find ∠AOB.

Answer 1

ABCD is a rectangle

With diagonal AC produced to point E.

We have

 ∠1 + ∠DCE = 180° (Linear pair)

∠1 + 146° = 180°

∠1 = 34°

We know that the diagonals of a parallelogram bisect each other.

Thus OC = OD

Also, angles opposite to equal sides are equal.

Therefore,

∠ODC = 34°

By angle sum property of a traingle

∠ODC +∠1 + COD = 180°

34° + 34° CPD = 180°

68° +∠COD = 180°

∠COD = 112°

Also, ∠CODand  ∠AOB are vertically opposite angles.

Therefore, ∠AOB = 112°

Hence, the required measure for  ∠AOBis 112°.