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# What is the angle of rotation of a pentagon?

## What is the angle of rotation of a pentagon?

The angle of rotation of an n sided regular polygon is given by 360∘n. A pentagon has 5 sides. ⟹Angle of rotation of a regular pentagon =360∘5=72∘. So, if you rotate the pentagon by an angle of 72∘, then it will look identical to the initial figure. Mathematics.

How do you calculate counterclockwise rotation?

Here are the rotation rules: 90° clockwise rotation: (x,y) becomes (y,-x) 90° counterclockwise rotation: (x,y) becomes (-y,x)

What is the rule for rotating counterclockwise by 180 degrees?

When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y). So all we do is make both x and y negative.

### What is the rule for a 270 degree counterclockwise rotation?

The rule for a rotation by 270° about the origin is (x,y)→(y,−x) .

What is angle of rotation of a polygon?

For rotation symmetry, the order of any regular polygon is the number of sides. The angle of rotation would be 360 degrees divided by that order. For example, an octagon is an 8-sided figure, so the order is eight. If you divide 360 by 8, you get 45, which means the octagon has an angle of rotation of 45 degrees.

Does a pentagon has a rotational symmetry?

A pentagon has 5 rotational symmetry as shown in figure has 5 point when rotated produces symmetrical image.

#### Is a 90 degree rotation clockwise or counterclockwise?

Since the rotation is 90 degrees, you will rotating the point in a clockwise direction.

What is the rule for a rotation of 90 degrees counterclockwise?

When we rotate a figure of 90 degrees counterclockwise, each point of the given figure has to be changed from (x, y) to (-y, x) and graph the rotated figure.

What is 90 degrees counterclockwise?

## What is the angle of rotation for this counterclockwise rotation about the origin?

270°
The point of rotation is the origin, draw lines joining one of the points, say X and it’s image to the origin. You can see that the lines form an angle of 270° , in the counterclockwise direction. Therefore, ΔX’Y’Z’ is obtained by rotating ΔXYZ counterclockwise by 270° about the origin.

How do you find the rotation of a polygon?

Coordinates of Rotation: The point (x,y) rotated an angle of θ counter-clockwise about the origin will land at point (x′,y′) where x′=xcos(θ)−ysin(θ) x ′ = x cos ⁡ ( θ ) − y sin ⁡ and y′=ycos(θ)+xsin(θ) y ′ = y cos ⁡ ( θ ) + x sin ⁡ .

How many order of rotation does a pentagon?

5
Therefore the order of rotational symmetry of a regular pentagon is 5. In fact, any manifestation of the regular pentagonal symmetry will have an order of 5.

### How many lines of rotational symmetry does a pentagon have?

5 lines of symmetry
Line symmetry in regular polygons A regular pentagon has 5 sides and 5 lines of symmetry.