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You are watching: If the smallest angle of rotation for a regular polygon is 18°, how many sides does polygon have?

The angle of rotational the opposite is the smallest angle for which the number can it is in rotated come coincide with itself. The bespeak of the contrary is the number of times the figure corresponds with itself together its rotates v 360° . Example: A constant hexagon has rotational symmetry.

Consider the constant pentagon ABCDE, with facility (of mass) O. The central angle O is a finish angle, therefore its measure is 360°. It is divided into 5 equal parts, so each of them has actually a measure up of 360°/5=72°.

Step-by-step explanation:

20

Step-by-step explanation:

The polygon has actually 20 sides (Icosagon)

Step-by-step explanation:

As the the smallest angle that rotation for a regular polygon is 18°, so a 18° rotation returns the exact same figure.

According come the attachment, the side abdominal muscle subtends an edge of 18° in ~ the centre. That is why a 18° rotation generates the same figure.

According to the nature of continuous polygon, And (as the radius of a continual polygon bisects the interior angle)

As in the triangle OAB,   So, So, interior angle the polygon is 162°

We recognize that, the inner angle of regular polygon with n side is, Hence,      Therefore, the polygon has 20 political parties (Icosagon) Since the sum of the angle is 360°, we should divide 360 with the number of sides that a polygon has.360/18=20; this polygon has actually 20 sides.Result:20

The the smallest angle of rotation is 18 degrees (Given)The total variety of degrees in 1 change is 360 degreesTherefore the total variety of angles consisting of the 360o is 360 / 18 = 20The polygon has 20 same sides (it is regular).

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