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Fantom [35]
2 years ago
10

Quadrilateral OPQR is inscribed in circle N, as shown below. Which of the following could be used to calculate the measure of ∠P

QR?
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.

(6x − 4)° + (2x + 16)° = 180°
(x + 16)° + (6x − 4)° = 180°
(6x − 4)° + (2x + 16)° = 360°
(x + 16)° + (6x − 4)° = 360°
Mathematics
2 answers:
Anna [14]2 years ago
8 0

The equation to be used to calculate the measure of ∠PQR in the cyclic quadrilateral is: (6x − 4)° + (2x + 16)° = 180°.

<h3>What are Opposite Angles in a Cyclic Quadrilateral?</h3>

A cylcic quadrilateral is a quadrilateral inscribed in a circle. The opposite angles are supplementary, that is they add up to give 180 degrees.

Thus, angles Q and O are opposite angles in the cyclic quadrilateral, which means they are supplementary.

Therefore, the equation to be used to calculate the measure of ∠PQR in the cyclic quadrilateral is: (6x − 4)° + (2x + 16)° = 180°.

Learn more about cyclic quadrilateral on:

brainly.com/question/10057464

sammy [17]2 years ago
5 0

Answer:

I just took the quiz and the answer above is NOT correct.

Step-by-step explanation:

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Try this solution:

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Step-by-step explanation:

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- the upstream speed is: V-Vc.

- according to the described above the distance for downstream is S1=(V+Vc)*t1, where t1=10; the distance for upstream is S2=(V-Vc)*t2, where t2=70.

- for whole travel down- and upstream: S=S1+S2.

- Using these it is possible to make up the system of the equations:

\left \{ {{(70(V-V_c)=10(V+V_c)} \atop {70(V-V_c)+10(V+V_c)=210}} \right.

V - the speed of the boat in still water - 6 miles per hour, Vc - the speed of the current - 4.5 miles per hour. All the details for the system of the equations are in the attachment.

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