Question

What is the sum of the interior angle measures in a 20-gon?

Answer 1

Sum of all interior angles of `20`-gon is `3240^@`

Explanation:

Three things first.

1. A polygon with `n` sides (`n`-gon) has `n` interior angles and `n` exterior angles.
2. As sum of each pair of exterior and interior angles is `180^@`, sum of all interior and exterior angles is `nxx180^@`
3. Sum of all the exterior angles of any polygon (i.e. irrespective of its number of sides) is always `360^@`.

Therefore `20`-gon has `20` exterior angles whose sum is `360^@`.

As such, sum of its all interior and exterior angles is `20xx180^@=3600^@`

Hence, sum of all interior angles is `3600^@-360^@=3240^@`