Question

Quadrilateral OPQR is inscribed in circle N, as shown below. Which of the following could be used to calculate the measure of ∠QRO? Circle N is shown with a quadrilateral OPQR inscribed inside it. Angle O is labeled x plus 16. Angle P is not labeled. Angle Q is labeled 6x minus 4. Angle R is labeled 2x plus 16. m∠QPO + (x + 16)° + (6x − 4)° = 360° m∠QPO = (x + 16)° + (6x − 4)° m∠QPO + (2x + 16)° = 180° m∠QPO = (6x − 4)° + (2x + 16)°

Answer 1

The sum of the opposite angles of the inscribed quadriateral is 180 degrees. The measure of ∠QRO is 64 degrees

Circle geometry

The sum of the opposite angles of the inscribed quadriateral is 180 degrees.

From the given diagram;

<O + <Q = 180

x + 16 + 6x - 4 = 180

7x + 12 = 180

7x = 168
x = 168/7

x = 24

Determine the measure of ∠QRO

∠QRO = 2x + 16
∠QRO = 2(24) + 16
∠QRO = 48 + 16

∠QRO = 64 degrees

Hence the measure of ∠QRO is 64 degrees

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