Convex hexagon ABCDEF is equiangular but has no two sides the same length. Its sides in some order are 1, 2, 3, 4, 5 and 6 units long. If AB=1 and CD>BC, what are the lengths of BC, CD, DE, EF and FA?
Another convex hexagon is also equiangular and has sided measuring 1, X, 3, 4, 5, and 6 units long in that order going clockwise. What is the measure of X?
Lets's place the vertex between the X and 3 sides at (0,0)
.
Let's place the next vertex at (3,0).
The next vertex is at (5,2√3).
The next, at (2.5,4.5√3).
The next, at (-3.5,4.5√3).
The last, at (-4,4√3).
Thus, the missing side measures √((-4)²+(4√3)²)=8.
Second part
