A regular decagon is rotated n degrees about its center, carrying the decagon onto itself. The value of n could be: 1. 10 degrees
2. 150 degrees
3. 225 degrees
4. 252 degrees

A decagon is a ten-sided polygon.

The value of n could be 252 degree.

Since, A Decagon has 10 sides

The angle made in one complete rotation is 360 degree.

Now find angle made in each rotation is,

Now, we have to find possible values of n.

Since, n must be a multiple of 36

Apply hit and trial from given option.

We observe that from given options, only 252 degree is multiple of 36.

Therefore, value of n could be 252 degree.

Hence, option 4  is correct.

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252°

Step-by-step explanation:

Given

Shape: Decagon

Required

Determine the value of n

A Decagon has 10 sides and a complete rotation takes 360°

First, we need to calculate the angle of each rotation as follows.

Each Rotation = ⅒ * 360°

Each Rotation = 360°

Next, we determine the possible values of n.

The statement is represented as "possible values of n" because n can assume infinite number of values.

However, n must be a multiple of 36

From the list of given options.

10, 150 and 225 are not multiples of 36

Only 252 happens to be a multiple of 36 from the list of given options.

Hence, option D answers the question [base on the given options]