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Points N, P, and R all lie on circle O. Arc PR measures 120°. Circle O is shown. Line segment P N is a diameter that extends outside of the circle to point Q. Line segment O R is a radius. Lines are drawn to connects point R to points P, O, N, and Q. Lines O R and N R are congruent. The length of P O is 5 and the length of R Q is 5 StartRoot 3 EndRoot. Arc P R measures 120 degrees. How does the measure of angle RNQ relate to the measure of arc PR? Angle RNQ is equal in measure to arc PR. Angle RNQ is half the measure of arc PR. Angle RNQ is twice the measure of arc PR. Angle RNQ is four times the measure of arc PR.

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taylorvierthaler

Answer:

A

Step-by-step explanation:

Lanuel

Based on the calculations, angle RNQ is equal in measure to arc PR by 120°.

Given the following data:

  • Angle RNO = 60°.
  • Side OR (radius) = 5.
  • Side RQ = 5√3.
  • Arc PR= 120°.

How to calculate the perimeter of a triangle.

Mathematically, the perimeter of a triangle is given by this formula:

[tex]P = a + b + c[/tex]

Where:

  • a, b, and c are length of sides.

Based on the diagram, we can deduce that side OQ is larger than RQ, thereby, making it a special right-angled triangle with 90-60-30 degree. Thus, side OQ have a length of 10 units and angle QOR is equal to 60°, while angle OQR is equal to 30°.

For the chord length:

[tex]Chord =2rsin(\frac{c}{2} )\\\\Chord =2\times 5 \times sin(\frac{60}{2} )\\\\Chord =10 \times sin30\\\\Chord =10 \times 0.5[/tex]

Chord = 5 units.

For angle RNQ:

Since the two (2) angles are supplementary, we have:

RNO + RNQ = 180°

[tex]60+RNQ=180\\\\RNQ=180-60[/tex]

RNQ = 120°.

Therefore, angle RNQ is equal to arc PR with a measure of 120°.

Read more on line segment here: brainly.com/question/18315903

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