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

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53
Oct 29, 2016

Answer:

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

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12
Mar 19, 2016

Answer:

#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^@#

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