Draw a Diagram and Look for a Pattern COURSE 2 LESSON 7-6 How many diagonals can be drawn inside a decagon? The goal is to find the number of diagonals that can be drawn inside a decagon. Remember that a diagonal is a segment that joins two vertices that are not endpoints of the same side of a polygon.The diagram below shows all the diagonals that can be drawn inside each polygon shown. 3 sides 4 sides 5 sides 6 sides 7-6

Draw a Diagram and Look for a Pattern COURSE 2 LESSON 7-6 (continued) Make a table to organize the information from the diagram. sides diagonals 3 4 2 5 6 9 The data in the table indicates that the formula for the number of diagonals that can be drawn inside a polygon of n sides is For a decagon, n = 10. n(n – 3) 2 10(10 – 3) = = 35 10 • 7 Thirty-five diagonals can be drawn inside a decagon. 7-6

Draw a Diagram and Look for a Pattern COURSE 2 LESSON 7-6 (continued) To check that 35 diagonals can be drawn inside a decagon, draw a diagram. There are 35 diagonals. 7-6

Draw a Diagram and Look for a Pattern COURSE 2 LESSON 7-6 Solve by drawing a diagram and looking for a pattern. The exterior angles of a triangle are the supplements of the interior angles, as shown. What is the sum of the exterior angles of a regular hexagon? 360º 7-6