Answer:
Minimum angle = 108°
Step-by-step explanation:
From the figure attached,
Minimum angle to overlap the star onto itself is the angle of rotation from point A to B.
Let the angle between A and B measure a°.
If we complete a star pentagon by joining the vertices of the star,
Formula to measure the internal angle of a polygon is,
Measure of internal angle = ![180\times \frac{(n-2)}{n}](https://tex.z-dn.net/?f=180%5Ctimes%20%5Cfrac%7B%28n-2%29%7D%7Bn%7D)
Measure of ∠ABC = ![\frac{(5-2)}{5}\times 180](https://tex.z-dn.net/?f=%5Cfrac%7B%285-2%29%7D%7B5%7D%5Ctimes%20180)
= 108°
Since, one side star divides the interior angle into three equal parts,
Measure of interior angle =
= 36°
From ΔAOB,
m(∠OAB) + m(∠AOB) + m(∠ABO) = 180° [Sum of interior angles of a triangle = 180°]
36° + a + 36° = 180°
a + 72° = 180°
a = 180 - 72
a = 108°
Therefore, by the minimum angle of rotation of 108° star will overlap onto itself.
You've certainly tried hard to describe it in enough detail so that
it can be answered without seeing the diagram. Sadly, it's not
enough.
We still don't know what's tangent to what, where point 'C' is, or
how any of this relates to a circle. You'll have to figure out some
way or us to see the diagram.