Quadrilateral opqr is inscribed inside a circle as shown below. what is the measure of angle o? you must show all work and calculations to receive credit. (10 points)

A quadrilateral inscribed in a circle is called a "cyclic quadrilateral."

A quadrilateral is cyclic, only if the sum of the measures of the opposite angles is 180°. 

Also, the reverse is true: If we know a quadrilateral to be cyclic, than its opposite angles must be supplementary (add up to 180°) .

Thus, we must have:



2x+(2x+4)=180

4x+4=180 (next dividing by 4:)

x+1=45

Thus, x=44, which means that the measure of angle O is 2x degrees, that is 88 degrees.

88°

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