Geometry CP Section 6-1: Angles of Polygons Page 1 of 2 Main ideas: Find the sum of the measures of the interior angles of a polygon to classify figures and solve problems. Find the sum of the measures of the exterior angles of a polygon to classify figures and solve problems. Standard: 12.0 What is the sum of the angles in a triangle? _____________ A __________________ is a simple closed figure in a plane formed by three or more line segments. A diagonal of a polygon is a segment that connects any two nonconsecutive vertices. For the polygons above, draw the diagonals from one vertex of each figure, and complete the table below. What pattern can you find in the table above? __________________________________________________________ Example 1: A convex polygon has 13 sides. Find the sum of the measures of the interior angles. Practice 1: Find the sum of the measures of the interior angles of each convex polygon. 1) 10-gon 2) 16-gon 3) 30-gon 4) 3x-gon Example 2: The measure of an interior angle of a regular polygon is 120. Find the number of sides. Practice 2: The measure of an interior angle of a regular polygon is given. Find the number of sides in each polygon. 5) 150 6)160 7) 175 Example 3: Find x Name of polygon Number of sides Number of triangles formed by diagonals Sum of the interior angles Triangle 3 1 (1 • 180)= 180 Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Quadrilateral
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Geometry CP Section 6-1: Angles of Polygons Page 1 of 2
Main ideas: Find the sum of the measures of the interior angles of a polygon to classify figures and solve
problems.
Find the sum of the measures of the exterior angles of a polygon to classify figures and solve
problems.
Standard: 12.0
What is the sum of the angles in a triangle? _____________
A __________________ is a simple closed figure in a plane formed by three or more line segments.
A diagonal of a polygon is a segment that connects any two nonconsecutive vertices. For the polygons above,
draw the diagonals from one vertex of each figure, and complete the table below.