Question

How many lines of symmetry does a regular decagon have?

Answer 1

Hint:
A Regular decagon is nothing but the figure having ten sides and ten vertex. In order to find the number of symmetries first draw a decagon and try to draw a line joining opposite vertices and then again draw the line from midpoint of a side to its opposite side mid-point and finally count the number of symmetries.

Complete step by step solution:
Here they have asked us to find the number of symmetry. Symmetry is nothing but a line that will split a shape into two parts, so that the two parts are mirror images of one another.
A Regular decagon is nothing but the figure having ten sides and ten vertex, which is shown as in the below diagram.

By looking at the figure of the decagon we can notice that the length of sides and angles are equal.
Now, try to draw a line which joins the two opposite vertices so that the line drawn makes a symmetry, as shown in the below diagram.

As shown in the above diagram if we draw a line joining opposite vertices we get exactly mirror images of one another. In the same way we draw all the possible lines joining opposite vertices as below.

In the above figure we have drawn \[5\] lines which join opposite vertices and we got \[5\] lines of symmetry.
As we can see all the sides of the decagon are equal and it is having the same angle, we can draw a line from the midpoint of a side joining the opposite side mid-point which gives a symmetry. Which is as shown in the below diagram.

In this case also we have \[5\] lines of symmetry.
Now, by combining both we get the total number of lines of symmetry of a decagon.
Therefore, if we add the number of lines of symmetry joining vertices with the number of lines of symmetry joining midpoints, we get a total of $10$ lines of symmetry, which is as shown in the below diagram.

In the above diagram, black line represents the line joining vertices and the red line joining midpoint.
Hence, a regular decagon has $10$ lines of symmetry.

Note:
Whenever they ask for lines of symmetry for a regular shape then one thing you have to remember is, in regular shapes the number of lines of symmetry is the same as that of the number of sides. Hence if we remember this point easily in no time we get the required answer.