Answer:
Option (3). 72°
Step-by-step explanation:
Angle of rotational symmetry = Central angle of a polygon
That means when we rotate the regular polygon by a central angle, polygon overlaps itself.
Central angle of a polygon with n sides =
Where n = number of sides of the polygon
Therefore, central angle of a polygon with 15 sides =
= 24°
Central angle tells us that after every 24° of rotation, polygon overlaps itself.
Angle of rotational symmetry may be 48°, 72°, 96°.....
Therefore, Option (3) is the possible angle of rotational symmetry.
SOLUTION
From the question given the following statements to prove are correct, then the last part
The reason is Side-side-side triangle theorem
This theorem states that all three sides of a triangle are congruent (identical) to the corresponding sides of another triangle, then the triangles themselves are also congruent.
Hence the answer is Side-side-side triangle theorem