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?
2 answers:
Answer:
Angle RNQ is equal in measure to arc PR.
Step-by-step explanation:
Consider the complete question is,
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.
By the below attached diagram,
In triangle PRN,
O∈PN,
Such that, RO = RN,
⇒ m∠RON = m∠RNO ......(1),
Also, m∠ROP+m∠RON = 180° ( linear pairs ),
⇒ 120° + m∠RON = 180°
⇒ m∠RON = 180° - 120° = 60°,
From equation (1),
m∠RNO = 60°,
Again,
m∠RNO + m∠RNQ = 180° ( linear pairs )
⇒ 60° + m∠RNQ = 180°
⇒ m∠RNQ = 180° - 60° = 120°,
But, Arc PR measures 120°
Hence, Angle RNQ is equal in measure to arc PR.
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The given function which models the value of Mark’s car, where x represents the number of years since he purchased the car.
We need to determine the approximate value of Mark's car after 7 years.
<u>Value of the car:</u>
The value of the car after 7 years can be determined by substituting x = 7 in the function , we get;
Rounding off to the nearest dollar, we get;
Thus, the approximate value of Mark's car after 7 years is $14278.
Hence, Option a is the correct answer.