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# Interior Angles Hall

### Study Guide for the Interior Angles of Polygons

Question | Answer |
---|---|

Explain how to use the number of sides to find the sum of the interior angles of polygons. | (n-2) x 180 = the sum of the interior angles of a polygon |

Explain how to use the number of sides to find one angle measure of a regular polygon. | (n-2) x 180 = the sum of the interior angles of a polygon. Divide this number by the number of sides. |

What are the differences between a regular and an irregular polygon? | Regular polygons have side and interior angle measurements that are are congruent.Irregular polygons do not have congruent side or interior angle measurements. |

Why is it important to know if a polygon is regular or irregular when determining angle measurements? | With regular polygons you can use the rule (n-2)x180/n. With irregular polygons you cannot use this rule because the angles are not congruent. |

Find the sum of the interior angles of a nonagon. | 1260 degrees |

Find the sum of the interior angles of a hexagon. | 720 degrees |

Find the sum of the interior angles of a decagon. | 1440 degrees |

Find the sum of the interior angles of a 18-gon. | 2880 degrees |

Find the measure of one interior angle for a regular pentagon. | 108 degrees |

Find the measure of one interior angle for a regular 12 sided figure. | 150 degrees |

Find the measure of one interior angle for a regular octagon | 135 degrees |

Explain how to use the number of sides to determine the number of triangles needed to triangulate the figure. | The number of sides minus 2 is equal to the number of triangles. |

Explain how triangulating a polygon can be used to find the sum of the interior angles of a polygon. | The number of triangles multiplied by the 180 is equal to the sum of the interior angles. |

What is the easiest way to triangulate a polygon? | Start from one vertex to draw non-intersecting diagonals. |

What is the measure of one angle of a regular hexagon? | 120 degrees |

What is the measure of one angle of a regular nonagon? | 140 degrees |

A regular pentagon and an irregular pentagon both have the same total interior angle measurement. True or False | True. It does not matter if a polygon is regular or irregular. The interior angle measure is always the same. |

Angles of a regular polygon are not equal. True or False | False. Regular polygons have angles with congruent measurements. |

Regular polygons have both congruent sides and congruent angles. True or False | True. Regular polygons have congruent angles and sides. |

A rectangle is a regular polygon. True or False | False. A rectangle has congruent angles, but it does not have congruent sides. |

A square is a regular polygon. True or False | True. A square has congruent angles and sides so it is a regular polygon. |

acute triangle | A triangle with all angles measures less than 90 degrees. |

isosceles triangle | A triangle with at least two congruent sides; two side lengths are the same. |

right triangle | A triangle with one 90 degree angle. |

scalene triangle | A triangle that has NO congruent sides; all side lengths are different. |

equilateral triangle | A triangle with three congruent sides; all side lengths have the same measure. |

obtuse | A triangle with one obtuse angle; one angle measure is greater than 90 degrees. |

triangle | A three sided polygon. |

triangle sum theorem | The theorem which states that the angles measures of any triangle must have a sum of 180 degrees; the angles of a triangle add up to 180 degrees. |

leg | In a right triangle, the legs are the two sides which create the right angle; the perpendicular line segments. |

hypotenuse | In a right triangle, the side opposite the right angle; the longest side in a right triangle. The side of the triangle that is does not create the right angle. |

triangle inequality | The rule that says the smallest side length plus the medium side length must have a sum greater than the largest side length. Small + Medium > Large |

3 sided shape | triangle |

4 sided shape | quadrilateral |

5 sided shape | pentagon |

6 sided shape | hexagon |

7 sided shape | septagon or heptagon |

8 sided shape | octagon |

9 sided shape | nonagon |

10 sided shape | decagon |

11 sided shape | hendecagon or an 11-gon |

12 sided shape | dodecagon |

15 sided shape | pentadecagon |

Sum of the interior angles of a polygon | (n-2) x 180 where n is the number of sides on the polygon |

Number of triangles formed when a polygon is divided into triangles using diagonals (triangulation) | n-2 (n is the number of sides) |

The measure of each interior angle of a regular polygon | Sum of the interior angles / number of sides |

Triangulate or Triangulation | The process of dividing a polygon into triangles by drawing its diagonals |

Polygon | A closed plane figure created by three or more line segments that intersect only at their endpoints (vertices) |

Regular Polygon | A polygon with congruent sides and angles |

Congruent | Having the same size and shape |

Explain how to use the number of sides to find the sum of the interior angles of polygons. | (n-2) x 180 = the sum of the interior angles of a polygon |

Explain how to use the number of sides to find one angle measure of a regular polygon. | (n-2) x 180 = the sum of the interior angles of a polygon. Divide this number by the number of sides. |

What are the differences between a regular and an irregular polygon? | Regular polygons have side and interior angle measurements that are are congruent.Irregular polygons do not have congruent side or interior angle measurements. |

Why is it important to know if a polygon is regular or irregular when determining angle measurements? | With regular polygons you can use the rule (n-2)x180/n. With irregular polygons you cannot use this rule because the angles are not congruent. |

Find the sum of the interior angles of a nonagon. | 1260 degrees |

Find the sum of the interior angles of a hexagon. | 720 degrees |

Find the sum of the interior angles of a decagon. | 1440 degrees |

Find the sum of the interior angles of a 18-gon. | 2880 degrees |

Find the measure of one interior angle for a regular pentagon. | 108 degrees |

Find the measure of one interior angle for a regular 12 sided figure. | 150 degrees |

Find the measure of one interior angle for a regular octagon. | 135 degrees |

Explain how to use the number of sides to determine the number of triangles needed to triangulate the figure. | The number of sides minus 2 is equal to the number of triangles. |

Explain how triangulating a polygon can be used to find the sum of the interior angles of a polygon. | The number of triangles multiplied by the 180 is equal to the sum of the interior angles. |

What is the easiest way to triangulate a polygon? | Start from one vertex to draw non-intersecting diagonals. |

Created by:
theboss1000