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Question 8 of 10True or False? A circle could be circumscribed about the quadrilateral below.B120°сOA. TrueA 90°OB. False60%D90°

Question 8 of 10True or False? A circle could be circumscribed about the quadrilateral-example-1
User Subaru Tashiro
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1 Answer

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17 votes

A circle can be circumscribed about a quadrilateral if the opposite angles are supplementary.

The quadrilateral in the figure in the question must satisfy the following conditions, therefore:


\begin{gathered} m\angle A+m\angle C=180\degree \\ m\angle B+m\angle D=180\degree \end{gathered}

We can make the check as follows:


\begin{gathered} 90+90=180 \\ 120+60=180 \end{gathered}

Therefore, a circle could be circumscribed about the quadrilateral.

The correct option is TRUE.

User Hamlet
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