Question

2. A Regular Octagon rotates counterclockwise about its center. At how many differentangles will the Octagon map onto itself?A regular Octagon has equal sides. Any rotations by multiples of degreesabout the center maps it onto itself.3. If a trapezoid is non-isosceles, then it has lines of reflection?4. A rectangle has 2 lines of symmetry which are also called

Answer 1

A regular Octagon is a Polygon with 8 equal sides.

Since the Octagon is a regular Octagon then all the sides are equal and all the interior angles are the same.

In one complete rotation (0-360 degree), the angles in which the regular octagon will map into itself can be derived by;

`d=(360)/(8)=45^0`

So, on an interval of 45 degree the Octagon maps onto itself.

Any rotation of 45 degree will map it onto itself.

The angle in which the regular octagon will map into itself are;

`45^0,90^0,135^0,180^0,225^0,270^0,315^0,360^0`

There are 8 different angles in which the Regular Octagon will map onto itself.

listed above are the 8 angles.