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Triangles 3 Exterior Angles Name __________________________ Date _______________ Period _______ Activity I. Discovering Exterior Angles of a Triangle The sides of the acute triangle at the right have been extended to form its exterior angles. 1. Which of the numbered angles in the figure are not exterior angles of the triangle? 1 3 4 2. How many exterior angles does a triangle have a) at one vertex? 2 6 5 9 8 b) altogether? 7 3. a) Is it possible that all of the triangle’s exterior angles of a triangle are equal? Explain. b) Is it possible that all of the triangle’s exterior angles of a triangle are unequal? Explain. II. Discovering the Triangle Exterior Angle Theorem (Remote Exterior Angle Theorem) 4. The sum of the interior angles of a triangle is _____________. U 3 5. Given CUP, identify: a) an exterior angle b) an interior angle adjacent to the exterior angle C 2 1 4 P c) 2 remote interior angles 6. On patty paper, trace and label the above triangle CUP with 1, 2, 3, and 4. 7. Tear off 2 and 3. Place them inside 4 so that the vertices all match up and 2 and 3 do not overlap. 8. What did you notice about 2, 3, and 4? 9. Make a conjecture about the relationship between an exterior angle and its 2 remote interior angles. Find the values of all variables. 10. 11. 12. 61° x° 39° 57 y° x° 48° 110 (y + 10) Page 1 of 2 Triangles 3 For problems 13-20, find x. Use your answers to work through the maze. Start at S. . 138 113 115 24 28 45 157 120 20 17 15 10 12 84 175 S 13. 14. x° 50° (3x)° x° 134° (7x) (3x) (7x)° 17. 33° (5x + 50) 90° 87° 91° 21° 15. (5x)° 34° 16. 20. 81 161 18 18. 83 151° x° x° 54° 19. x° 95° 148° The ratio of angles of a triangle is 20:30:30. Find the measure of the smallest angle of the triangle. Page 2 of 2 Triangles 3 Triangle 3 Activity Key 1. 2, 5, 8 2. a) 2 b) 6 3. a) Yes, if the triangle is an equilateral triangle then all exterior angles would measure 120º. b) Yes, if all the interior angle measures in the triangle are different then all of the exterior angle measures would be different. 4. 180º 5. a) 4 b) 1 c) 2, 3 8. 2 and 3 fit perfectly into 4 9. The exterior angle of a triangle equals the sum of the two remote interior angles. 10. x = 100 11. x = 42, y = 28 12. y = 117 13. 84 14. 12 15. 10 16. 120 17. 24 18. 113 19. 138 20. 45º Page 3 of 2