In the given figure, sides AD and AB of cyclic quadrilateral ABCD are produced to E and F respectively.

Question:

In the given 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:

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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