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Q.

What is the value of x?

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a

55°

b

28°

c

47°

d

35°

answer is C.

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Detailed Solution

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It can be seen in the given figure that ∠DCB and ∠DCX form a linear pair.

∴ ∠DCB + ∠DCX = 180°

⇒ ∠DCB + 139° = 180°

⇒ ∠DCB = 180° − 139° = 41°

It is known that opposite angles of a cyclic quadrilateral are supplementary.

∴ ∠DAB + ∠DCB = 180°

⇒ 3x − 2° + 41°= 180°

⇒ 3x + 39° = 180°

⇒ 3x = 180° − 39° = 141°

x=13×141°=47°

Thus, the value of x is 47°.

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