Question

Which figure shows the rotation image of pentagon A after a 216 $^0$ clockwise rotation about its center?

Answer 1

Hint: In this question, we are given a regular pentagon (which has all sides equal). Now, according to the question we need to determine which of the options have a rotation of ${216^0}$. To do this find the value of 1 rotation by dividing 360 degrees with the number of sides then multiply it with 1,2,3 and 4 and use the elimination method to find the figure with rotation = 216$^0$ to find the correct answer to the problem.

Complete step-by-step answer:
As we know that after the one rotation of the pentagon = \[\dfrac{{360}}{5} = {72^0}\]
Thus, in figure one, the pentagon is showing 1 rotation and thus = \[{72^0}\]
Similarly, in figure two the rotation of pentagon will be 2 times the one rotation of pentagon i.e. $2 \times {72^o} = {144^o}$
Similarly, In figure three the rotation of pentagon will be 3 times the one rotation of pentagon i.e. $3 \times {72^o} = {216^o}$
Also In figure four, the rotation of pentagon will be 4 times the one rotation of pentagon i.e. $4 \times {72^o} = {288^o}$
Thus, in figure three the rotation of the pentagon will be ${216^0}$.

Note: In the above question which was based on the pentagon shape which shows some properties i.e. The sum of the interior angles in the pentagon is equal to 540 °. This is a regular polygon if all the sides are equal and all the angles are of equal proportion. In a regular polygon, the inside angle is of 108 °, and the outside angle is 72 °. The equilateral pentagon has five sides which are identical.