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Q.

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


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a

70∘,120∘,110∘,60∘

b

120∘,110∘,70∘,60∘

c

110∘,700∘,60∘,120∘

d

60∘,120∘,70∘,110∘  

answer is A.

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Detailed Solution

Consider the given question,
ABCDis a cyclic quadrilateral. We know that,
In a cyclic quadrilateral, the sum of opposite angles is 180∘and sum of all the angles = 360∘.
Option 1: 70∘,120∘,110∘,60∘ Sum of Opposite angles:
 ∠A+∠C=70°+110°=180∘ and ∠B+∠D=120°+60°=180∘.
The opposite angles are 180∘and sum of all the angles is 360∘.
Option 2: 120∘,110∘,70∘,60∘ Sum of Opposite angles:
 ∠A+∠C=120°+70°=190∘≠180o and ∠B+∠D=110°+60°=170∘≠180o.
The opposite angles are not 180∘.
Option 3: 110∘,700∘,60∘,100∘ Sum of Opposite angles:
 ∠A+∠C=110°+60°=170∘≠180o and ∠B+∠D=700°+100°=800∘≠180o.
The opposite angles are not 180∘.
Option 4: 60∘,120∘,70∘,110∘ Sum of Opposite angles:
 ∠A+∠C=60°+70°=130∘≠180o and ∠B+∠D=120°+110°=230∘≠180o.
The opposite angles are not 180∘.
Hence, the angles of the cyclic quadrilateral are 70∘,120∘,110∘,60∘.
Therefore, option 1 is correct.
 
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