1. FINDING MISSING ANGLE MEASURES part 1

2.  Use the definitions and relationships of complementary, supplementary, adjacent, and vertical angles to determine missing angle measures. LEARNING TARGET 2

3. Let’s Review…Vertical Angles are not adjacent, are formed by two intersecting lines, and are congruent (equal). Angles A and B are Vertical and therefore the same angle measure. VERTICAL ANGLES

4. We can use the definition of Vertical Angles to find the measures of other angles. How to Find the Missing Angle Measure: All vertical angles are congruent (equal) and therefore equal to each other. If Angle A is 35°, then Angle B is also 35°.

5. Find the angle measure of each missing angle. VERTICAL ANGLES

6. COMPLEMENTARY ANGLES Let’s Review…Complementary Angles are two angles whose sum is 90°. a b

7. How to Find the Missing Angle Measure: Calculate the measure of the missing angle so that the sum of the two angles equals 90°. 27° + b = 90° b = 63° COMPLEMENTARY ANGLES

8. Find the measure of the missing angle. COMPLEMENTARY ANGLES

9. SUPPLEMENTARY ANGLES a b Let’s Review…Supplementary Angles are two (or more) angles whose sum is 180°.

10. How to Find the Missing Angle Measure: Calculate the measure of the missing angle so that the sum of the two angles equals 180°. 155° + b = 180° b = 25° SUPPLEMENTARY ANGLES

11. Find the measure of the missing angle. SUPPLEMENTARY ANGLES

12. Find the Supplement of each angle. SUPPLEMENTARY ANGLES AngleSupplement Your Angle + X = 180° 50°130° 110°70° 65°115° 26°154°

13. Find the Complement of each angle. COMPLEMENTARY ANGLES AngleComplement Your Angle + X = 90° 50°40° 110°Impossible 65°25° 26°64°

14. TIME TO PRACTICE

15. 1) Find the missing angle. 36° ?° FIND THE MISSING ANGLE

16. 1) Find the missing angle. 36° ?° Relationship: Complementary 90° – 36° = 54° FIND THE MISSING ANGLE

17. 2) Find the missing angle. 64° ?° FIND THE MISSING ANGLE

18. 2) Find the missing angle. 64° ?° Relationship: Complementary 90 ° – 64° = 26° FIND THE MISSING ANGLE

19. 5) Find the missing angle. ?° 168° FIND THE MISSING ANGLE

20. 5) Find the missing angle. ?° 168° Relationship: Supplementary 180° – 168° = 12° FIND THE MISSING ANGLE

21. 6) Find the missing angle. 58° ?° FIND THE MISSING ANGLE

22. 6) Find the missing angle. 58° ?° Relationship: Supplementary 180° – 58° = 122° FIND THE MISSING ANGLE

23. 35º ?º?º

24. FIND THE MISSING ANGLE 35º ?º?º Relationship: Vertical 35° = 35°

25. FIND THE MISSING ANGLE 140º ?º?º

26. FIND THE MISSING ANGLE 140º ?º?º Relationship: Vertical 140° = 140°

27. Part 2 FINDING A MISSING ANGLE AND X

28.  Sometimes the lines between Geometry and Algebra blur just a bit. For example, sometimes the missing angle is not just a letter but a problem to be solved. Let’s take a look. We know that the two angles are supplementary…but how do we solve for X. When we solve these types of problems we are going to have TWO ANSWERS…what does X equal and what is the measure of the missing angle. FINDING THE MISSING ANGLE…WITH X.

29. FIND THE MISSING ANGLE AND X  We begin by figuring out what the two angles need to equal when added together. In this case…180° Angle 1 + Angle 2 = 180 30 + 2x = 180 (We can solve this…no problem) 2x = 150 X = 75 So the angle is 2x = 2(75) = 150°

30. 3) Solve for x. 3x° 2x° FIND THE MISSING ANGLE AND X What is the relationship? What do the two terms need to equal?

31. 3) Solve for x. 3x° 2x° 3x° + 2x° = 90° 5x = 90 x =18 FIND THE MISSING ANGLE AND X 2x°= 2(18) = 36° 3x° = 3(18) = 54°

32. 7) Solve for x. 4x° 5x° What is the relationship? What do the two terms need to equal? FIND THE MISSING ANGLE AND X

33. 7) Solve for x. 4x° 5x° 4x° + 5x° = 180° 9x° = 180° x = 20 FIND THE MISSING ANGLE AND X 5x° = 5(20) = 100° 4x° = 4(20) = 80°

34. 8) Solve for x. 2x + 103x + 20 (2x + 10) + (3x + 20) = 180 Combine Like Terms 5x + 30 = 180 Solve for X 5x = 150 x = 30 FIND THE MISSING ANGLE AND X X = 30 3(30) + 20 = 110° X = 30 2(30) + 10 = 70°

35. 4) Solve for x. 2x + 5 x + 25 FIND THE MISSING ANGLE AND X What is the relationship? What do the two terms need to equal?

36. 4) Solve for x. 2x + 5 x + 25 (2x + 5) + (x + 25) = 90Combine Like Terms 3x + 30 = 90 Solve for X 3x = 60 x = 20 FIND THE MISSING ANGLE AND X X = 20 20 + 25= 45 X = 20 2(20) + 5 = 45

37. FIND THE MISSING ANGLE AND X