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Salsk061 [2.6K]
3 years ago
5

Determine whether each regular polygon tessellates the plane. Explain.

Mathematics
2 answers:
BlackZzzverrR [31]3 years ago
7 0

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.

kondaur [170]3 years ago
3 0

Answer:

b.  no; measure of interior angle = 135°

Step-by-step 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,

\frac{360}{135}= 2.66 Its not a complete number this is why octagons do not tessellate.

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