1. Triangles and Lines – Sum of the Angles in a Triangle The sum of the angles in any triangle = 180°

2. Triangles and Lines – Sum of the Angles in a Triangle The sum of the angles in any triangle = 180° 105 ° 40 ° 35 ° 33 ° 67 °

3. Triangles and Lines – Sum of the Angles in a Triangle The sum of the angles in any triangle = 180° 105 ° 40 ° 35 ° 33 ° 67 ° So given a triangle, and any two angles, you could find the third angle.

4. Triangles and Lines – Sum of the Angles in a Triangle The sum of the angles in any triangle = 180° 105 ° 40 ° 35 ° 33 ° 67 ° So given a triangle, and any two angles, you could find the third angle.

5. Triangles and Lines – Sum of the Angles in a Triangle 48° x EXAMPLE # 1 : Find the missing angle in the triangle.

6. Triangles and Lines – Sum of the Angles in a Triangle 48° x EXAMPLE # 1 : Find the missing angle in the triangle.

7. Triangles and Lines – Sum of the Angles in a Triangle 15° x EXAMPLE # 2 : Find the missing angle in the triangle. 28°

8. Triangles and Lines – Sum of the Angles in a Triangle 15° x EXAMPLE # 2 : Find the missing angle in the triangle. 28°

9. Triangles and Lines – Sum of the Angles in a Triangle 150° x EXAMPLE # 3 : Find the missing angle in the triangle. 70°

10. Triangles and Lines – Sum of the Angles in a Triangle 150° x EXAMPLE # 3 : Find the missing angle in the triangle. 70° We must first find the supplementary angle for this linear pair… ?

11. Triangles and Lines – Sum of the Angles in a Triangle 150° x EXAMPLE # 3 : Find the missing angle in the triangle. 70° We must first find the supplementary angle for this linear pair… ?

12. Triangles and Lines – Sum of the Angles in a Triangle 150° x EXAMPLE # 3 : Find the missing angle in the triangle. 70° We must first find the supplementary angle for this linear pair… 30°

13. Triangles and Lines – Sum of the Angles in a Triangle x 92° EXAMPLE # 4 : Find the missing angle. 56°

14. Triangles and Lines – Sum of the Angles in a Triangle x 92° EXAMPLE # 4 : Find the missing angle. 56° 32° First find the missing angle in the triangle…

15. Triangles and Lines – Sum of the Angles in a Triangle x 92° EXAMPLE # 4 : Find the missing angle. 56° 32° These are a linear pair so 180°- 32° = 148° …

16. Triangles and Lines – Sum of the Angles in a Triangle 148° 92° EXAMPLE # 4 : Find the missing angle. 56° 32° Do you see it ?

17. Triangles and Lines – Sum of the Angles in a Triangle 148° 92° EXAMPLE # 4 : Find the missing angle. 56° 32° Do you see it ? Theorem – the measure of an exterior angle of a triangle is equal to the sum of the opposite interior angles.

18. Triangles and Lines – Sum of the Angles in a Triangle x 39° EXAMPLE # 5 : Find the missing angle. 115°

19. Triangles and Lines – Sum of the Angles in a Triangle x 39° EXAMPLE # 5 : Find the missing angle. 115°

20. Triangles and Lines – Sum of the Angles in a Triangle x 85° EXAMPLE # 6 : Find the missing angle. 51°

21. Triangles and Lines – Sum of the Angles in a Triangle x 85° EXAMPLE # 6 : Find the missing angle. 51° Theorem – the measure of an exterior angle of a triangle is equal to the sum of the opposite interior angles.