Question

A regular polygon has interior angles that are 5 times larger than each of its exterior angles. How many sides does the polygon have?

Answer 1

`12`

Explanation:

The exterior angles of a dodecagon are `30^@`, so they sum to `12xx30^@ = 360^@`

The interior angles are `150^@ = 180^@ - 30^@ = 5 xx 30^@`

Answer 2

We need to be able to calculate this, without having to consider the size of the exterior and interior angles of all the different polygons.

Explanation:

Let the size of an exterior angle be `x°`
The size of the interior angle is therefore `5x°`

An exterior and interior angle are supplementary angles.

`x° + 5x° = 180° rArr 6x = 180°`

`x = 30°` This is size of each exterior angle (`ext angle`)

The sum of the exterior angles is 360°

Number of sides (or angles) = `360/(ext angle)`
`360/30 = 12` sides