Answer quick points n, p, and r all lie on circle o. arc pr measures 120° how does the measure of angle rnq relate to the measure of arc pr? a. angle rnq is equal in measure to arc pr. b. angle rnq is half the measure of arc pr. c. angle rnq is twice the measure of arc pr. d. angle rnq is four times the measure of arc pr.

Option A. Angle RNQ is equal in measure to arc PR.

Step-by-step explanation:

we know that

The triangle NOR is an equilateral triangle, because has three equal sides

NO=OR=RN > radius of the circle O

therefore

The interior angles of the triangle NOR measures 60 degrees each

so

∠RNO=60°

Find the measure of angle RNQ

we have that

∠RNO+∠RNQ=180° > by supplementary angles (linear pair)

substitute

60°+∠RNQ=180°

∠RNQ=180°-60°=120°

we know that

arc PR= 120° > see the graph

therefore

∠RNQ=arc PR

Angle RNQ is equal in measure to arc PR.

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