Find the number of sides of polygon if...? All the angle of a polygon are either #155^o# or #140^o#. There are twice as many angles of #155^o# as #140^o#.

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Answer 1 · 2017-05-26T19:42:36

#12#

The external angles of the polygon are each #180^@-theta# where #theta# is the corresponding internal angle.

So the external angles are a mixture of:

#180^@-155^@ = 25^@#

#180^@-140^@ = 40^@#

with twice as many #25^@#'s as #40^@#'s.

We can deduce that the number of angles and sides is a multiple of #3#, each set of #3# consisting of:

#2*25^@+40^@ = 90^@#

external angles.

The external angles of the polygon add up to #360^@ = 4*90^@#, so there are four sets of three angles/sides. That is #12# sides.