The Polygon Angle-Sum Theorem

NUMBER OF SIDES NAME 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon

The Polygon Angle-Sum Theorem A diagonal is a segment that connects two nonconsecutive vertices in a polygon!

The Polygon Angle-Sum Theorem Essential Understanding: The sum of the interior angle measures of a polygon depends on the number of sides the polygon has. By dividing a polygon with n sides into (n – 2) triangles, you can show that the sum of the interior angle measures of any polygon is a multiple of 180.

The Polygon Angle-Sum Theorem Problem 1: Finding a Polygon Angle Sum What is the sum of the interior angle measures of a heptagon?

The Polygon Angle-Sum Theorem Problem 1b: Finding a Polygon Angle Sum What is the sum of the interior angle measures of a 17-gon?

The Polygon Angle-Sum Theorem Problem 1c: The sum of the interior angle measures of a polygon is 1980. How can you find the number of sides in the polygon? Classify it!

The Polygon Angle-Sum Theorem Problem 1d: The sum of the interior angle measures of a polygon is 2880. How can you find the number of sides in the polygon? Classify it!!!

The Polygon Angle-Sum Theorem

The Polygon Angle-Sum Theorem

The Polygon Angle-Sum Theorem Problem 2: What is the measure of each interior angle in a regular hexagon?

The Polygon Angle-Sum Theorem Problem 2b: What is the measure of each interior angle in a regular nonagon?

The Polygon Angle-Sum Theorem Problem 2c: What is the measure of each interior angle in a regular 100-gon? Explain what happens to the interior angles of a regular figure the more sides the figure has? What is the value approaching but will never get to?

The Polygon Angle-Sum Theorem Problem 3: What is m<Y in pentagon TODAY?

The Polygon Angle-Sum Theorem Problem 3b: What is m<G in quadrilateral EFGH?

The Polygon Angle-Sum Theorem You can draw exterior angles at any vertex of a polygon. The figures below show that the sum of the measures of exterior angles, one at each vertex, is 360.

Problem 4: What is m<1 in the regular octagon below?

What is the measure of an exterior angle of a regular pentagon? Problem 4b: What is the measure of an exterior angle of a regular pentagon?

Problem 5: What do you notice about the sum of the interior angle and exterior angle of a regular figure?

Problem 6: If the measure of an exterior angle of a regular polygon is 18. Find the measure of the interior angle. Then find the number of sides the polygon has.

Problem 6b: If the measure of an exterior angle of a regular polygon is 72. Find the measure of the interior angle. Then find the number of sides the polygon has.

Problem 6c: If the measure of an exterior angle of a regular polygon is x. Find the measure of the interior angle. Then find the number of sides the polygon has.