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What will be the value of x if in the given figure, the cyclic quadrilateral has sides AB and AC with AD, AB are produced to E, F respectively?

Given that $∠ C B F = 1500$ and $∠ C D E = x 0$ .

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answer is A.

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Detailed Solution

It is given that the cyclic quadrilateral has sides AB and AC with AD, AB are produced to E, F respectively.
We have to find x.
Question Image

It is known that the exterior angle of a cyclic quadrilateral is equal to the opposite interior angle and also the sum of angles on a straight line is equal to

1800

.
We know that,

∠ C B F = 1500

and

∠ C D E = x 0

.
Also, the exterior angle of a cyclic quadrilateral is equal to the opposite interior angle. Therefore,

e x t e r i o r ∠ C B F = intertior ∠ CDA ⇒ ∠ CDA=150 0

As EDA is a straight line,

⇒ ∠ CDA+ ∠ CDE=180 0

Putting,

∠ CDA=150 0

and calculating the value of the angle

∠ C D E = x 0

x +150 0 =180 0 ⇒ x = 300

So, the value of

x = 300

.
Therefore, option 1 is correct.

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