1. The goal is to find the number of diagonals that can be drawn inside a decagon. How many diagonals can be drawn inside a decagon? COURSE 2 LESSON 7-6 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 sides4 sides5 sides6 sides Draw a Diagram and Look for a Pattern 7-6

2. (continued) COURSE 2 LESSON 7-6 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) 2 = = 35 10 7 2 Thirty-five diagonals can be drawn inside a decagon. Make a table to organize the information from the diagram. sides diagonals 3030 4242 5555 6969 Draw a Diagram and Look for a Pattern 7-6

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

4. 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 Draw a Diagram and Look for a Pattern 7-6