Question

Which rotation about its center will carry a regular decagon onto itself?

A. 54
B. 162
C. 198
D. 252
Please explain!!!

Answer 1

To find which rotation will carry a regular decagon onto itself, you must determine a whole number multiple of 36 degrees, which corresponds to the angle of rotational symmetry for a decagon. The only option that is a multiple of 36 is 252 degrees.

Step-by-step explanation:

The question involves a regular decagon, which is a polygon with 10 equal sides and 10 equal angles. To find which rotation will carry the decagon onto itself, you need to know that a full rotation is 360 degrees. Since the decagon is regular, it has rotational symmetry, meaning it will coincide with itself multiple times during a full rotation.

By dividing the 360 degrees by the number of sides (10), we find that every 36 degrees, the decagon will match itself. A rotation must be a multiple of 36 degrees to carry the decagon onto itself. Let's analyze the options given:

• 54 degrees: This is not a multiple of 36.
• 162 degrees: This is 4.5 times 36, which is not a whole number multiple.
• 198 degrees: This is 5.5 times 36, also not a whole number multiple.
• 252 degrees: This is 7 times 36, which is a whole number multiple.

Therefore, the correct answer is 252 degrees, option D.

Answer 2

D.252

Step-by-step explanation:

In this question, We have to find which rotation about its center will carry a regular decagon onto itself?

A decagon : 10 sided polygon

As we know, a full rotation can be 360°.

For a decagon: 360/10 =36

For a decagon, any multiple of 36 can map onto itself.

In our options only 252 is the multiple of 36.

So, correct answer is option D 252