Answer:
The correct option is A
Therefore the quadrilateral in the option A can be inscribed in a circle.
Step-by-step explanation:
Given:
Four Quadrilateral, A ,B ,C ,D in the figure below.
For a quadrilateral to be inscribed in a circle we required opposite angles must be supplementary, that is it should add up to 180°.
So from the four given quadrilateral we have only in quadrilateral A the opposite angles are supplementary.
Quadrilateral A :
Consider the quadrilateral PQRS where
∠SPQ = 91°
∠PQR = 101°
∠QRS = 89°
∠SPQ and ∠QRS are opposite angles and their sum is 180°
[tex]\angle SPQ+\angle QRS = 91+89 =180[/tex]
Others in option B, C , and D opposite angles are not supplementary hence cannot inscribe in a circle.
Therefore the quadrilateral in the option A can be inscribed in a circle.
