MathDB

A piece of paper is folded in half. A second fold is made at an angle

\phi

(

0^\circ < \phi < 90^\circ

) to the first, and a cut is made as shown below. 12881 When the piece of paper is unfolded, the resulting hole is a polygon. Let

O

be one of its vertices. Suppose that all the other vertices of the hole lie on a circle centered at

O

, and also that \angle XOY \equal{} 144^\circ, where

X

and

Y

are the the vertices of the hole adjacent to

O

. Find the value(s) of

\phi

(in degrees).

Problem Statement