1. Types of Angles
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2. Definition: An Angle is the union of two rays that share an end-point.
The rays of the angles are the sides of the angle.
The common end-point is called the vertex.

3. Denoting angles
The following angle is denote as ∠ABC A B C

4. Protractor
A protractor is used to measure an angle in degrees.

5. Worksheet:
Measuring angles using a protractor.

6. Angles There are Six types of angles Right angle Straight angle
Acute angle
Obtuse angle
Reflex Angle
Full Rotation

7. Right Angles
Forms a square corner
Forms a 90 degree angle.
90 degrees

8. RIGHT ANGLES
measure exactly 90 °
The “square” symbol means 90’

9. Straight Angle
Forms a straight line
Angle is 180 degrees
180 degrees

10. STRAIGHT ANGLE is exactly 180 ° A straight angle is 180 degrees
This is a straight angle

11. Worksheet
Straight angles.

12. Acute Angles Forms an angle that is less than a right angle
Angle is less than 90 degrees

13. ACUTE ANGLES
are less than 90°

14. Obtuse Angles Form an angle that is more than a right angle
Angle is more than 90 degrees

15. OBTUSE ANGLES
are greater than 90 ° but less than 180 °

16. FULL ROTATION A full rotation is 360 degrees
The angle around a point is 3600

17. Reflex Angle A Reflex Angle is more than 180° but less than 360°
This is a reflex angle

18. Worksheet
Angles around a point.

19. CONGRUENT CONGRUENT means identical in form/same shape and size.
CONGRUENT LINE SEGMENTS means two line segments are of equal length.
CONGRUENT Angles means two angles are of equal measure. ● ● ● ●

20. Theorems
If two angles are right, then they are congruent.

21. Angle Bisector
A ray that divides an angle into 2 congruent adjacent angles.
BD is an angle bisector of <ABC. A D B C

22. Ex: If FH bisects EFG & mEFG=120o, what is mEFH?

23. Solve for x, given that BD bisects ∠ABC.
* If they are congruent, set them equal to each other, then solve! D A
x+40o
x+40 = 3x-20
40 = 2x-20
60 = 2x
30 = x
3x-20o C B

24. Supplementary, and Complementary Angles

25. Adjacent angles
Adjacent angles are angles that share the same vertex and a common side.
15º
45º

26. These are examples of adjacent angles.
45º
80º
35º
55º
130º
50º
85º
20º

27. These angles are NOT adjacent.
100º
50º
35º
35º
55º
45º

28. Supplementary angles add up to 180º.
40º
120º
60º
140º
Adjacent and Supplementary Angles
Supplementary Angles but not Adjacent

29. Supplementary Angles - Two angles whose measures add up to 180 degrees
Supplementary Angles - Two angles whose measures add up to 180 degrees. Supplementary angles can be placed so that they form a straight line.
Example: angle A = 80 degrees and angle B = 100 degrees. Then angle A + angle B = 180 degrees. We can say that angles A and B are supplementary.

30. Complementary angles add up to 90º.
30º
40º
50º
60º
Adjacent and Complementary Angles
Complementary Angles but not Adjacent

31. Complementary Angles - Two angles whose measures add up to 90 degrees.
Example: angle A = 30 degrees and and angle B = 60 degrees. Then angle A + angle B = 90 degrees. We can say angles A and B are complementary.

32. Example:
If ∠AOC is a right angle, and m ∠AOB is 85o find m ∠BOC.

33. Example: Solve for x

34. Exercise:
Find the measure of an angle if its measure is 24 degrees more than the measure of its complement.

35. Theorem:
If two angles are complements of the same angle, then they are congruent.
If two angles are congruent, then their complements are congruent.

36. Don’t change your radius!
Construction #1
Construct a segment congruent to a given segment.
This is our compass.
Given: A B
Procedure:
1. Use a straightedge to draw a line. Call it l.
Construct: XY = AB
2. Choose any point on l and label it X.
Don’t change your radius!
3. Set your compass for radius AB and make a mark on the line where B lies. Then, move your compass to line l and set your pointer on X. Make a mark on the line and label it Y. l X Y

37. Construct an angle congruent to a given angle
Construction #2
Construct an angle congruent to a given angle
Procedure: A C B
Given:
1) Draw a ray. Label it RY. D
2) Using B as center and any radius, draw an arc intersecting BA and BC. Label the points of intersection D and E. E
Construct:
3) Using R as center and the SAME RADIUS as in Step 2, draw an arc intersecting RY. Label point E2 the point where the arc intersects RY D2
4) Measure the arc from D to E. R Y
5) Move the pointer to E2 and make an arc that that intersects the blue arc to get point D2 E2
6) Draw a ray from R through D2

38. Bisector of a given angle?
Construction #3
How do I construct a
Bisector of a given angle? C A B Z
Given: X Y
Procedure:
Using B as center and any radius, draw
and arc that intersects BA at X and BC at point Y.
2. Using X as center and a suitable radius, draw and arc.
Using Y as center and the same radius, draw an arc
that intersects the arc with center X at point Z.
3. Draw BZ.