A regular polygon has 15 sides. Which is a possible angle of rotational symmetry for the figure? 12° 45° 72° 90°
2 answers:
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.
You might be interested in
Answer: The quadrilateral HIJK is a parallelogram.
Explanation:
It is given that the coordinates of the vertices for the figure HIJK are H(0, 5), I(3, 3), J(4, –1), and K(1, 1).
The parallelogram diagonal theorem states that the quadrilateral is a parallelogram if both diagonal bisects each other.
If HIJK is a quadrilateral, then HJ and IK are the diagonals of HIJK.
First we find the midpoint of HJ.
Now, find the midpoint of IK.
The midpoint of both diagonal are same. It means the diagonals of HIJK bisects each other.
By parallelogram diagonal theorem, we can say that the quadrilateral HIJK is a parallelogram.
I hope this helps you
