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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 =
Measure of ∠ABC =
= 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.
