Answer:
(D)[tex]x=104^{\circ}[/tex]
Step-by-step explanation:
Given: It is given that circle O is circumscribed about quadrilateral ABCD such that ∠ABC=91° and ∠ADC=x-15°.
To find: the value of x.
Solution: It is given that circle O is circumscribed about quadrilateral ABCD such that ∠ABC=91° and ∠ADC=x-15°.
We know that the sum of opposite angles of the cyclic quadrilateral is 180°, therefore
[tex]{\angle}ABC+{\angle}ADC=180^{\circ}[/tex]
Substituting the given values, we have
[tex]91^{\circ}+x-15^{\circ}=180^{\circ}[/tex]
[tex]x+76^{\circ}=180^{\circ}[/tex]
[tex]x=104^{\circ}[/tex]
thus, the value of x is [tex]104^{\circ}[/tex].
Hence, option D is correct.
