Question

Each exterior angle of a regular polygon is 18 degrees. How many sides does the polygon have?

Answer 1

Hint: In this problem, we have to find the number of sides of a regular polygon which has an exterior angle of \[{{168}^{\circ }}\]. We know that if we find the size of an exterior angle for the given regular polygon whose exterior angle is \[{{18}^{\circ }}\], we can find the number of sides. We know that for a regular polygon the exterior angle of any side is equal to \[{{360}^{\circ }}\div \theta =n\], we can substitute the given exterior angle in this formula to find the number of sides.

Complete step-by-step answer:
We know that the given regular polygon has exterior angles of \[{{18}^{\circ }}\].
We know that if we find the size of an exterior angle for the given regular polygon whose exterior angle is \[{{18}^{\circ }}\], we can find the number of sides.
\[\Rightarrow {{360}^{\circ }}\div \theta =n\] …….. (1)
Where, n is the number of sides.
We can now substitute the above value of \[\theta \] in (1), we get
\[\Rightarrow {{360}^{\circ }}\div {{18}^{\circ }}=20\]
Therefore, there are 20 sides in the given regular polygon whose exterior angle is \[{{168}^{\circ }}\].

Note: Students make mistakes while finding the exterior angle from the exterior angle by subtracting the given angle with \[{{180}^{\circ }}\] which is substituted to the formula for the number of sides. We should also know that if we know the number of sides, we can find the size of the exterior angle and vice versa.