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Which of the following pairs of angles are opposite angles of a cyclic quadrilateral?

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131 °, 28 °

95 °, 55 °

123 °, 57 °

64 °, 52 °

answer is C.

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Detailed Solution

We have to find the pair of angles given in the option are opposite angles of a cyclic quadrilateral or not.
Consider the following diagram.
Question Image

We know that, the sum of opposite angles of every cyclic quadrilateral is

180 °

.
If

ABCD

is cyclic quadrilateral, then

∠ A + ∠ C = 180 °

.
The sum of the angles

123 °

and

57 °

is equal to

180 °

.
Except for option (3), the sum of the two angles specified in the other options are not

180 °

.
Thus, the pairs of angles are 1

23^{\circ}

and

57^{\circ}

.
Hence, the correct option is 3.

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