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 = [tex]180\times \frac{(n-2)}{n}[/tex]
Measure of ∠ABC = [tex]\frac{(5-2)}{5}\times 180[/tex]
= 108°
Since, one side star divides the interior angle into three equal parts,
Measure of interior angle = [tex]\frac{108}{3}[/tex] = 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.
