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.
You might be interested in
Answer:
2x -y ≥ 4
Step-by-step explanation:
The intercepts of the boundary line are given, so it is convenient to start with the equation of that line in intercept form:
... x/(x-intercept) + y/(y-intercept) = 1
... x/2 + y/(-4) = 1
Multiplying by 4 gives the equation of the line.
... 2x -y = 4
This line divides the plane into two half-planes. The half-plane that is shaded is the one for larger values of x and/or smaller values of y than the ones on the line. So, for some given y, if we increase x we will get a number from our equation above that is greater than 4. Hence, the inequality we want is ...
... 2x -y ≥ 4
We use the ≥ symbol because the line is solid, so part of the solution space.
