1. FINDING MISSING ANGLE MEASURES part 1

2. 02.04.2019 Agenda Bell Ringer Bell Ringer Jaguar Ascensions (Homeroom)
Introduction Video
Cornell Notes
Topic: Finding the missing angle
Essential Question: How can special angle relationships be used to solve equations for multistep problems?
Student/Teacher Dialog

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

4. Angles A and B are Vertical and therefore the same angle measure.
VERTICAL ANGLES
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.

5. How to Find the Missing Angle Measure:
VERTICAL ANGLES
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°.

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

7. Let’s Review…Complementary Angles are two angles whose sum is 90°.b

8. COMPLEMENTARY ANGLES
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°

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

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

11. SUPPLEMENTARY ANGLES
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°

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

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

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

15. Time to Practice

16. 1) Find the missing angle.?°
36°

17. 1) Find the missing angle.?°
36°
Relationship: Complementary
90° – 36° = 54°

18. 2) Find the missing angle.?°
64°

19. 2) Find the missing angle.?°
64°
Relationship: Complementary
90 ° – 64° = 26°

20. 5) Find the missing angle.
168° ?°

21. 5) Find the missing angle.
168° ?°
Relationship: Supplementary
180° – 168° = 12°

22. 6) Find the missing angle.?°
58°

23. 6) Find the missing angle.?°
58°
Relationship: Supplementary
180° – 58° = 122°

24. FIND THE MISSING ANGLE ?º
35º

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

26. FIND THE MISSING ANGLE ?º
140º

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

28. FINDING A MISSING ANGLE AND X
Part 2

29. FINDING THE MISSING ANGLE…WITH X.
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.

30. 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°

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

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

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

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

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

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

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

38. FIND THE MISSING ANGLE AND X

39. Reference
mpmsjaguars.weebly.com/uploads/1/3/3/7/ /missing_angles_good.ppt