Study Guide for the Interior Angles of Polygons
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| 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
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| 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.
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| 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.
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| 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.
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| Find the sum of the interior angles of a nonagon. | 1260 degrees
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| Find the sum of the interior angles of a hexagon. | 720 degrees
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| Find the sum of the interior angles of a decagon. | 1440 degrees
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| Find the sum of the interior angles of a 18-gon. | 2880 degrees
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| Find the measure of one interior angle for a regular pentagon. | 108 degrees
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| Find the measure of one interior angle for a regular 12 sided figure. | 150 degrees
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| Find the measure of one interior angle for a regular octagon | 135 degrees
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| 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.
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| 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.
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| What is the easiest way to triangulate a polygon? | Start from one vertex to draw non-intersecting diagonals.
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| What is the measure of one angle of a regular hexagon? | 120 degrees
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| What is the measure of one angle of a regular nonagon? | 140 degrees
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| 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.
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| Angles of a regular polygon are not equal. True or False | False. Regular polygons have angles with congruent measurements.
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| Regular polygons have both congruent sides and congruent angles. True or False | True. Regular polygons have congruent angles and sides.
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| A rectangle is a regular polygon. True or False | False. A rectangle has congruent angles, but it does not have congruent sides.
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| A square is a regular polygon. True or False | True. A square has congruent angles and sides so it is a regular polygon.
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| acute triangle | A triangle with all angles measures less than 90 degrees.
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| isosceles triangle | A triangle with at least two congruent sides; two side lengths are the same.
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| right triangle | A triangle with one 90 degree angle.
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| scalene triangle | A triangle that has NO congruent sides; all side lengths are different.
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| equilateral triangle | A triangle with three congruent sides; all side lengths have the same measure.
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| obtuse | A triangle with one obtuse angle; one angle measure is greater than 90 degrees.
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| triangle | A three sided polygon.
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| 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.
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| leg | In a right triangle, the legs are the two sides which create the right angle; the perpendicular line segments.
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| 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.
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| 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
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| 3 sided shape | triangle
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| 4 sided shape | quadrilateral
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| 5 sided shape | pentagon
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| 6 sided shape | hexagon
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| 7 sided shape | septagon or heptagon
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| 8 sided shape | octagon
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| 9 sided shape | nonagon
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| 10 sided shape | decagon
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| 11 sided shape | hendecagon or an 11-gon
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| 12 sided shape | dodecagon
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| 15 sided shape | pentadecagon
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| Sum of the interior angles of a polygon | (n-2) x 180 where n is the number of sides on the polygon
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| Number of triangles formed when a polygon is divided into triangles using diagonals (triangulation) | n-2 (n is the number of sides)
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| The measure of each interior angle of a regular polygon | Sum of the interior angles / number of sides
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| Triangulate or Triangulation | The process of dividing a polygon into triangles by drawing its diagonals
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| Polygon | A closed plane figure created by three or more line segments that intersect only at their endpoints (vertices)
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| Regular Polygon | A polygon with congruent sides and angles
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| Congruent | Having the same size and shape
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| 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
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| 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.
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| 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.
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| 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.
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| Find the sum of the interior angles of a nonagon. | 1260 degrees
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| Find the sum of the interior angles of a hexagon. | 720 degrees
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| Find the sum of the interior angles of a decagon. | 1440 degrees
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| Find the sum of the interior angles of a 18-gon. | 2880 degrees
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| Find the measure of one interior angle for a regular pentagon. | 108 degrees
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| Find the measure of one interior angle for a regular 12 sided figure. | 150 degrees
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| Find the measure of one interior angle for a regular octagon. | 135 degrees
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| 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.
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| 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.
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| What is the easiest way to triangulate a polygon? | Start from one vertex to draw non-intersecting diagonals.
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