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Exploring Angle Measures of Polygons The sum of the interior angles in a triangle is ___________. 1) a) Draw an equilateral triangle. An equilateral triangle is a regular polygon. Side lengths in your equilateral triangle ____________ b) What is the measure of each interior angle of an equilateral triangle? 2) a) Draw a square. Side lengths in your square ____________ b) Draw a diagonal between two non-adjacent corners so the square is divided into triangles. c) How many triangles are created? d) What is the sum of the interior angles of a square? e) What is the measure of each interior angle of a square? This means not side by side. 3) Repeat step 2 for a regular pentagon and a regular hexagon. (Note: You will need to draw more than one diagonal to divide each shape into triangles.) a) Regular Pentagon Side lengths in your regular pentagon ____________ i. Draw a diagonal between two non-adjacent corners so the pentagon is divided into triangles. ii. How many triangles are created? iii. What is the sum of the interior angles of a regular pentagon? iv. What is the measure of each interior angle of a regular pentagon? b) Regular Hexagon Side lengths in your regular hexagon ____________ i. Draw a diagonal between two non-adjacent corners so the hexagon is divided into triangles. ii. How many triangles are created? iii. What is the sum of the interior angles of a regular hexagon? iv. What is the measure of each interior angle of a regular hexagon? 4) Complete the following table for the shapes that you drew from steps 1 to 3. Figure Equilateral triangle Number of Sides Number of Triangles Sum of Interior Angles 1 3 180° Measure of Each Interior Angle Square Regular pentagon Regular hexagon 5) a) Do you notice any patterns in the table? State the patterns that you see? b) Without making a sketch, determine the sum of the interior angles of these regular polygons. • An 8 sided figure _______________ • A 10 sided figure _______________ • A 20 sided figure _______________ c) Without making a sketch, determine the measure of each interior angle of these regular polygons. • An 8 sided figure _______________ • A 10 sided figure _______________ • A 20 sided figure _______________ d) Fill out the chart below. Number of Sides Figure Sum of Interior Angles Measure of Each Interior Angle 8-sided regular polygon 10-sided regular polygon 20-sided regular polygon e) What is the name of an 8 sided polygon? _________________ 10 sided polygon? 20 sided polygon? _______________ ______________