Question

The sum ofthe interior angles of a polygon is 3960°.(1) find the number of sides of the polygon (2) find the size of its exterior angel?

Answer 1

Number of sides of polygon is `24` and if polygon is regular, size of each exterior angle is `15^@`

Explanation:

A polygon has as many pairs of interior and exterior as number of its sides. Further each pair of exterior and interior add up to `180^@`.

Sum of all the exterior angles of any polygon is `360^@`

As sum of all the interior angles of the polygon is `3960^@`

Sum of all pairs of exterior and interior angles is `3960^@+360^@=4320^@`

As each pair is `180^@`, number of sides of polygon is `(4320^@)/(180^@)=24`

Sum of exrerior angles is always `360^@` and if polygon is regular (i.e. all sides andangles are equal), size of each exterior angle is `(360^@)/24=15^@`