The circle is divided into

Question

\[360\] equal parts. Point
\[O\] represents the center of the circle.
A circle with center point O and four rays. Ray OL points halfway between 3 and 4 o'clock. Ray OM points to 2 o'clock. Ray ON points to 12 o'clock. Ray OP points to 8 o'clock.
\[O\]
\[M\]
\[N\]
\[P\]
\[L\]
A circle with center point O and four rays. Ray OL points halfway between 3 and 4 o'clock. Ray OM points to 2 o'clock. Ray ON points to 12 o'clock. Ray OP points to 8 o'clock.
Which angle measures
\[120\degree\]?
Choose 1 answer:
Choose 1 answer:
(Choice A)
\[\angle{POM}\]
A
\[\angle{POM}\]
(Choice B)
\[\angle{NOP}\]
B
\[\angle{NOP}\]
(Choice C)
\[\angle{LON}\]
C
\[\angle{LON}\]

Answer 1

To find the angle measure of \[\angle POM\], we need to subtract the measure of \[\angle PON\] from the measure of \[\angle NOM\].

Since \[\angle NOM\] points from 12 o'clock to 2 o'clock, it covers \[\frac{2}{12} = \frac{1}{6}\] of the circle, which is \[\frac{1}{6} \cdot 360\degree = 60\degree\].

Similarly, \[\angle PON\] points from 12 o'clock to 8 o'clock, so it covers \[\frac{4}{12} = \frac{1}{3}\] of the circle, which is \[\frac{1}{3} \cdot 360\degree = 120\degree\].

Therefore, the measure of \[\angle POM\] is \[60\degree - 120\degree = -60\degree\].

Since angles cannot be negative, none of the given choices have a measure of \[120\degree\].