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Deducing Properties of Parallelogram

In the given ...

Question

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

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Solution

ABCD is a rectangle

With diagonal AC produced to point E.

We have

(Linear pair)

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

Thus

Also, angles opposite to equal sides are equal.

Therefore,

By angle sum property of a traingle

Also, and are vertically opposite angles.

Therefore,

Hence, the required measure for is .

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In the figure, ABCD is a rectangle in which diagonal AC is produced to E. If $∠ E C D = 146^{\circ}$ , find $∠ A O B$ .

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