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Quadrilateral OPQR is inscribed in circle N, as shown below. Which of the following could be used to calculate the measure of ∠OPQ? m∠OPQ + (2x + 16)° = 180° m∠OPQ = (6x − 4)° + (2x + 16)° m∠OPQ + (x + 16)° + (6x − 4)°= 360° m∠OPQ = (x + 16)° + (6x − 4)°

Quadrilateral OPQR is inscribed in circle N as shown below Which of the following could be used to calculate the measure of OPQ mOPQ 2x 16 180 mOPQ 6x 4 2x 16 m class=

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Answer:

m∠OPQ + (2x + 16)° = 180°

Explanation:

In the figure, Quadrilateral OPQR is inscribed in circle N, thus, OPQR is a cyclic quadrilateral.

By circle's theorem, the opposite angles of a cyclic quadrilateral add up to 180 degrees, therefore, the equation that could be used to calculate the measure of ∠OPQ is

[tex]m\angle OPQ+(2x+16)\degree=180\degree[/tex]

The first option is correct.

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