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Question

In the figure, sides AD and AB of cyclic quadrilateral ABCD are produced to E and F respectively. If CBF=130 and CDE=x, find the value of x.


Solution

ANSWER:
ABCD is a cyclic quadrilateral.
We know that in a cyclic quadrilateral, the exterior angle is equal to the interior opposite angle.
∴ ∠ CBF = ∠ CDA
⇒ ∠ CBF = (180 ° – x)
⇒ 130 ° = 180 ° – x [∵ ∠ CBF = 130 °]
⇒ x = (180 ° – 130 ° ) = 50 °
Hence, x = 50 °

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