Sum of Angles in Polygons.  A polygon is a two-dimensional (flat) shape that has all straight lines. It needs to be closed, meaning there is an inside.

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Presentation transcript:

Sum of Angles in Polygons

 A polygon is a two-dimensional (flat) shape that has all straight lines. It needs to be closed, meaning there is an inside and outside.  Examples of polygons:  Things that are not polygons:

 In order to determine the sum of the angles in any shape, we can divide it into triangles and then add all of those together to find the total.  However, this does not work if our triangles meet in the middle and create new angles that were not there before.  In this picture, new angles were created in the middle which is why it seems like there are 180° when the outside shape only has 360°

Name# of sides# of trianglesCalculationTotal sum of angles Triangle31180° Quadrilateral42180° x 2360° Pentagon53180° x 3540° Hexagon64180° x 4720° Heptagon75180° x 5900° Octagon86180° x 61080°

 Without drawing a picture, how many degrees do the angles in a nonagon (9 sides) add up to?  The angles in a nonagon (9 sides) add up to _____.  Without drawing a picture, how many degrees do the angles in a decagon (10 sides) add up to?  The angles in a decagon (10 sides) add up to _____.

 Without drawing a picture, how many degrees do the angles in a nonagon (9 sides) add up to?  The angles in a nonagon (9 sides) add up to 1260°.  Without drawing a picture, how many degrees do the angles in a decagon (10 sides) add up to?  The angles in a decagon (10 sides) add up to 1440°.

 Formula for total number of degrees in a polygon: total degrees = (n – 2) x 180°, where n is the number of sides this is how many this is how many degrees triangles there are each triangle is (two fewer than the number of sides)

Direct Station  We will continue in our notes.  We will look at how to find single angles in polygons now that we know the formula for the total number of angles.

Independent Station  You are going to use one of the Pearson interactives in order to learn about the relationship between angles and sides in triangles.  You will need to open up the Google Form and Pearson at the same time and switch back and forth. The directions/questions are on the Google Form but you will need to use the Pearson interactive to help answer them.