1. Concept 1

2. Concept 2

3. Example 1 Use the Triangle Angle-Sum Theorem SOFTBALL The diagram shows the path of the softball in a drill developed by four players. Find the measure of each numbered angle. UnderstandExamine the information in the diagram. You know the measures of two angles of one triangle and only one measure of another. You also know that  1 and  2 are vertical angles.

4. Example 1

5. Use the Triangle Angle-Sum Theorem Answer: Therefore, m  1 = 63, m  2 = 63, and m  3 = 38. CheckThe sums of the measures of the angles in each triangle should be 180. m  1 + 43 + 74= 63 + 43 + 74 or 180 m  2 + m  3 + 79= 63 + 38 + 79 or 180

6. A.A B.B C.C D.D Example 1 A.95 B.75 C.57 D.85 Find the measure of  3.

7. Concept 3

8. Concept 4

9. Example 2 Use the Exterior Angle Theorem GARDENING Find the measure of  FLW in the fenced flower garden shown. Answer: So, m  FLW = 2(80) – 48 or 112.

10. A.A B.B C.C D.D Example 2 A.30 B.40 C.50 D.130 The piece of quilt fabric is in the shape of a right triangle. Find the measure of  ACD.

11. Concept 5

12. Example 3 Find Angle Measures in Right Triangles Find the measure of each numbered angle.

13. Example 3

14. m  1 = 104, m  2 = 76, m  3 = 42, m  4 = 48, m  5 = 49

15. A.A B.B C.C D.D Example 3 A.50 B.45 C.85 D.130 Find m  3.