QQuestion
ABCD is a cyclic quadrilateral. If ∠ADB = x° and ∠ABD = y° then ∠BCD is (x + y)°.
✓Answer
True
Explanation:
In cyclic quadrilateral ABCD, opposite angles are supplementary.
So, ∠BAD + ∠BCD = 180°.
In triangle ABD, the three angles are ∠ABD = y°, ∠ADB = x°, and ∠BAD.
Therefore, ∠BAD = 180° − (x + y).
Now, substitute this into the first equation:
∠BCD = 180° − ∠BAD
= 180° − [180° − (x + y)]
= (x + y)°.
Hence, ∠BCD = (x + y)°.
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