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$ABCD$ is a cyclic quadrilateral, then the angles of the quadrilateral in the same order are:

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70^{\circ}, 120^{\circ}, 110^{\circ}, 60^{\circ}

120^{\circ}, 110^{\circ}, 70^{\circ}, 60^{\circ}

110^{\circ}, 700^{\circ}, 60^{\circ}, 120^{\circ}

60^{\circ}, 120^{\circ}, 70^{\circ}, 110^{\circ}

answer is A.

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Detailed Solution

Consider the given question,

ABCD

is a cyclic quadrilateral. We know that,
In a cyclic quadrilateral, the sum of opposite angles is

180^{\circ}

and sum of all the angles

=

360^{\circ}

.
Option 1:

70^{\circ}, 120^{\circ}, 110^{\circ}, 60^{\circ}

Sum of Opposite angles:

∠ A + ∠ C = 70 ° + 110 ° = 180^{\circ}

and

∠ B + ∠ D = 120 ° + 60 ° = 180^{\circ}

.
The opposite angles are

180^{\circ}

and sum of all the angles is

360^{\circ}

.
Option 2:

120^{\circ}, 110^{\circ}, 70^{\circ}, 60^{\circ}

Sum of Opposite angles:

∠ A + ∠ C = 120 ° + 70 ° = 190^{\circ} \neq 180^{o}

and

∠ B + ∠ D = 110 ° + 60 ° = 170^{\circ} \neq 180^{o}

.
The opposite angles are not

180^{\circ}

.
Option 3:

110^{\circ}, 700^{\circ}, 60^{\circ}, 100^{\circ}

Sum of Opposite angles:

∠ A + ∠ C = 110 ° + 60 ° = 170^{\circ} \neq 180^{o}

and

∠ B + ∠ D = 700 ° + 100 ° = 800^{\circ} \neq 180^{o}

.
The opposite angles are not

180^{\circ}

.
Option 4:

60^{\circ}, 120^{\circ}, 70^{\circ}, 110^{\circ}

Sum of Opposite angles:

∠ A + ∠ C = 60 ° + 70 ° = 130^{\circ} \neq 180^{o}

and

∠ B + ∠ D = 120 ° + 110 ° = 230^{\circ} \neq 180^{o}

.
The opposite angles are not

180^{\circ}

.
Hence, the angles of the cyclic quadrilateral are

70^{\circ}, 120^{\circ}, 110^{\circ}, 60^{\circ}

.
Therefore, option 1 is correct.

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ABCD is a cyclic quadrilateral, then the angles of the quadrilateral in the same order are:

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$ABCD$ is a cyclic quadrilateral, then the angles of the quadrilateral in the same order are: