It's a simple method:

Graphics[Map[HalfLine, 
  Partition[
   AnglePath[
    Prepend[ 
     Table[{(2 Sin[18 Degree])^n, -108 Degree}, {n, 1, 
       10}], {1, -72 Degree}]], 2, 1]]]

But this method has a lot of extra half-lines. The following code works better:

Graphics[{Pink, Opacity[0.4], EdgeForm[Dashed], 
  Map[Triangle, 
   Partition[
    AnglePath[
     Prepend[Table[{(2 Sin[18 Degree])^n, -108 Degree}, {n, 1, 
        10}], {1, -72 Degree}]], 3, 1]]}]

It's a simple method:

Graphics[Map[HalfLine, 
  Partition[
   AnglePath[
    Prepend[ 
     Table[{(2 Sin[18 Degree])^n, -108 Degree}, {n, 1, 
       10}], {1, -72 Degree}]], 2, 1]]]

But this method has a lot of extra half-lines. The following code works better:

Graphics[{Opacity[
   0.6], {Table[FaceForm[RandomColor[]], 10], 
    Map[Triangle, 
     Partition[
      AnglePath[
       Prepend[Table[{(2 Sin[18 Degree])^n, -108 Degree}, {n, 1, 
          10}], {1, -72 Degree}]], 3, 1]]}\[Transpose]}]

It's a simple method:

Graphics[Map[HalfLine, 
  Partition[
   AnglePath[
    Prepend[ 
     Table[{(2 Sin[18 Degree])^n, -108 Degree}, {n, 1, 
       10}], {1, -72 Degree}]], 2, 1]]]

But I can't get rid of the extra half-lines.

It's a simple method:

Graphics[Map[HalfLine, 
  Partition[
   AnglePath[
    Prepend[ 
     Table[{(2 Sin[18 Degree])^n, -108 Degree}, {n, 1, 
       10}], {1, -72 Degree}]], 2, 1]]]

But this method has a lot of extra half-lines. The following code works better:

Graphics[{Pink, Opacity[0.4], EdgeForm[Dashed], 
  Map[Triangle, 
   Partition[
    AnglePath[
     Prepend[Table[{(2 Sin[18 Degree])^n, -108 Degree}, {n, 1, 
        10}], {1, -72 Degree}]], 3, 1]]}]