Question

Determine whether each regular polygon tessellates the plane. Explain.

octagon
a.
yes; measure of interior angle = 135°
b.
no; measure of interior angle = 135°
c.
yes; measure of interior angle = 45°
d.
no; measure of interior angle = 45°

Answer 1

The exterior angle is always supplemental (adds up to 180°). So if the interior angle is 135°, the exterior angle will be 45°. This is because an exterior angle is formed by extending one side out and measuring the new exterior angle.

Answer 2

b. no; measure of interior angle = 135°

Explanation:

A regular polygon can only tessellate the plane when its interior angle divides 360 degrees.

The polygons that tessellate are - the square, the equilateral triangle, and the regular hexagon.

The octagon cannot tessellate because its internal angle does not divide 360 degrees. Tessellation means an arrangement of polygons in a repeated pattern without overlapping.

The internal angle of an octagon is 135 degrees. When we divide 360 by 135 we get,

`(360)/(135)= 2.66` Its not a complete number this is why octagons do not tessellate.