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.

1 Answer
May 26, 2017

12

Explanation:

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.