Angles...

the middle part is a pentagon [polygon].

formula for sum of interior angles of a polygon=(no of sides - 2)*180.

so the sum of interior angles in the middle polygon = (5 - 2)*180 = 540 degree.

so each angle is 540/5 = 108 .

so the adjacent angle in the smaller triangle is 180 - 108 = 72.

that smaller triangle is with 2 equal length side (isosceles) i.e two equal angles and that angle is also 72.

so alpha is 180 - 72 - 72 = 36

As each angle of a regular pentagon is 108 degrees, both base angles of the triangles are 180-108=72 degrees. This alpha is 180-2*(72)=36.

$\frac{total\ angles}{number\ of\ sides}$ $=$ $\frac{180}{5}$ $=$ $36$