Circle O is shown below. The diagram is not drawn to scale. If m<R=24, what is m<O?
A. 48* my answer
B. 96*
C. 24*
D. 12*
48 is right, and if you have other numbers, the answer is just double m<r. Hope this helps! Congrats on getting to the end of geometry :)
Since the diagram is not drawn to scale, we cannot rely on the size of the angles based on their appearance. However, we can use the properties of circles to determine the relationship between angle R (m<R) and angle O (m<O).
In a circle, the measure of an angle formed by two chords is equal to half the sum of the measures of the intercepted arcs.
Since angle R (m<R) intercepts arc OR, and angle O (m<O) also intercepts arc OR, we have:
m<R = m<O
So if m<R = 24 degrees, then m<O must also be 24 degrees.
Therefore, the correct answer is C. 24 degrees.
To find the measure of angle O, we need to apply the properties of angles formed by intersecting chords in a circle.
In this case, we know that the angle formed by chords R and O is equal to half the sum of the measures of the intercepted arcs.
Since we are given that m<R = 24, we know that the measure of the intercepted arc for chord R is also 24.
Then, the measure of the intercepted arc for chord O is the entire circle minus the intercepted arc of chord R, which is 360 - 24 = 336 degrees.
Since the angle formed by chords R and O is equal to half the sum of the measures of the intercepted arcs, we have:
m<O = (24 + 336)/2 = 360/2 = 180 degrees.
Therefore, the measure of angle O is 180 degrees.
So, the correct answer is C. 24 degrees.