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Q: Which of these two regular polygons has the larger interior angle?

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The octagon. The rule is that as the number of sides of a regular polygon increases then the external angle decreases while the interior angle increases The summation of the interior and external angleof one vertex is 180o.

No regular polygon can have an interior angle of 180 degrees or more. No regular polygon can have an interior angle of 180 degrees or more. No regular polygon can have an interior angle of 180 degrees or more. No regular polygon can have an interior angle of 180 degrees or more.

In a tessellation a number of polygons meet at a point. If n polygons meet, then there will be n vertices. These must add up to 360 degrees so that the tessellation does not leave holes. So the interior angles of the polygon must be a factor of 360 degrees. Interior angle of an equilateral triangle = 60 deg = 360/6 and so it will tessellate; Interior angle of a square = 90 deg = 360/4 and so it will tessellate; Interior angle of a regular pentagon = 108 deg which is not a factor of 360 and so it will not tessellate; etc.

For regular polygons, all the interior angles are the same measure, while the sum of the exterior angles is always 360 for any regular polygon. Use these facts and the fact that each interior/exterior angle pair has a sum of 180 to answer this question. 360 divided by 8 = 45. So each exterior angle of the figure measures 45. 180 - 45 = 135, so each interior angle measures 135 degrees.

If the exterior angle is 30o then the shape has 360/30 = 12 sides. An interior angle = 180 - exterior angle = 180 - 30 = 150. Since the shape has 12 sides the interior angles sum to 150 x 12 = 1800o.

Related questions

pentagon

Hexagon.

Pentagon.

A pentagon

heptagon

An equilateral triangle is the only polygon in which the exterior angle is larger than the interior angle. They are equal in a square and smaller in all regular polygons with more sides,

Each interior angle of a square is 90 degrees Each interior angle of a regular pentagon is 108 degrees

It is the regular heptagon which has the larger interior angle. The rule is that as the number of sides of a regular polygon increases then the external angle decreases while the interior angle increases The summation of the interior and external angleof one vertex is 180 degrees.

If, by longer, you mean larger, the answer is a heptagon.

Each vertex angle of a polygon is composed of an external angle and an interior angle. These two angles are supplementary (total 180°). As the number of sides of a regular polygon increases then the external angle decreases and conversely, the interior angle increases. The interior angle of a regular pentagon (108°) is larger than the interior angle of a square (90°).

A polygon with any number of sides can have an exterior angle that is larger than the corresponding interior angle. However, a triangle is the only regular polygon where the exterior angle is larger.

The octagon. The rule is that as the number of sides of a regular polygon increases then the external angle decreases while the interior angle increases The summation of the interior and external angleof one vertex is 180o.

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