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?**