If a circle is circumscribed around a quadrilateral, as

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If a circle is circumscribed around a quadrilateral, as shown above, what is the value of \(x\)?

1) \(z=100\) and \(w=95\).
2) \(y=85\).

OA A

If a quadrilateral is inscribed in a circle (such as the one shown in the diagram), then the opposite angles of the quadrilateral are supplementary, i.e., the measures of the opposite angles add up to 180 degrees. Therefore, here we have x + z = 180 and w + y = 180. Therefore, if we know the value of z, then we can determine the value of x.

Statement One Only:

z = 100 and w = 95.

Since z = 100 and x + z = 180, x = 180 - 100 = 80. Statement one alone is sufficient to answer the question.

Statement Two Only:

y = 85

Since angle x is an adjacent angle to angle y, not the opposite angle of angle y, we can’t determine the value of x. Statement two alone is not sufficient to answer the question.

Answer: A