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