
The operation above rotates the regular pentagon clockwise by (72
n) degrees from its center. What replaces the initial
b position when
n = 4?
A. a
B. b
C. c
D. d
E. e
(C) Think of the polygon as you would a wheel being rotated at its center. A wheel sweeps a 360º angle everytime it returns to its initial positon. Since this is a regular pentagon, we can increment our rotations by dividing 360/5 = 72.
So everytime the center spins 72º clockwise, the polygon moves by one vertex. So, when
n = 4 the pentagon rotates by 4 vertices and the initial
b position is replaced by
c or answer choice (C).
An alternative way to consider the problem is to realize that everytime
n = 5, it returns to its original configuration. So, when
n = 4, the position is occupied by the vertex that is one vertex away in the clockwise direction because it lags by one 72º turn.
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"Since this is a regular pentagon, we can increment our rotations by
dividing 360/5 = 72. So everytime the center spins 72º clockwise, the polygon moves by one vertex."
Doesn't pentagon has 540 degrees?