Chapter 6.3, Problem 17WE

To determine

To prove: that there is no regular polygon with an interior angle whose measure is $155°$ .

Explanation of Solution

An indirect proof is initiated by assuming temporarily that whatever is need to prove is untrue and then work from there to finally conclude that the assumption is untrue.

Proof:

Assume temporarily that there is a $n$ sided polygon with an interior angle $155°$ .

Then, each exterior angle of this polygon would be $25°$ .

There are $25n$ exterior angles.

The sum of exterior angles of a regular polygon is $360°$ .

Therefore, $25n=360°$

However, there is no whole number $n$ which would satisfy this equation.

Hence, initial assumption is not true.

Therefore, there is no regular polygon with an interior angle whose measure is $155°$ .