MathematicsIn the figure, if A,B,Cand D are vertices of cyclic quadrilateral, then which of the following is the measure of ∠x?

In the figure, if $A, B, C$ and $D$ are vertices of cyclic quadrilateral, then which of the following is the measure of $∠ x$ ?

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A
$70^{0}$
B
$35^{0}$
C
$110^{0}$
D
$100^{0}$

Solution:

Consider the given figure,

∠ CBA + 70^{0} = 180^{0}

(linear pair)
Then,

∠ CBA = 180^{0} - 70^{0}

∠ CBA = 110^{0}

∵ ABCD

is cyclic quadrilateral.
Sum of opposite angles of a cyclic quadrilateral is

180^{o}

.
Thus,

∠ CBA + ∠ CDA = 180^{0}

⟹

110^{0} + ∠ CDA = 180^{0}

⟹

∠ CDA = 180^{0} - 110^{0}

⟹

∠ CDA = 70^{0}

Now,

∠ x + ∠ CDA = 180^{0}

(linear pair)

⟹

∠ x + 70^{0} = 180^{0}

⟹

∠ x = 110^{0}

Hence, the measure of

∠ x

110^{0}

.
Therefore, option 3 is correct.

In the figure, if $A, B, C$ and $D$ are vertices of cyclic quadrilateral, then which of the following is the measure of $∠ x$ ?

Solution:

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