1. Angles Review

2. This powerpoint presentation will allow you to work at your own pace through various angle problems.

3. When you see this symbol at the top of the screen, you are just supposed to read an explanation or “watch” the problem being solved.

4. When you see this symbol at the top of the screen, it’s your turn to try a problem. You’ll have the opportunity to check your answers at the end of the presentation.

5. Angle Vocabulary These are the words that you need to know for your angles test. AngleVertexSide Adjacent Angles Acute Angle Vertical Angles Obtuse Angle Right AngleStraight Angle

6. Write the vocabulary word that matches the definition. 1. the common endpoint of two rays that form an angle 2. An angle whose measure is exactly 90  3. Two coplanar angles that have a common endpoint and a common side but do not overlap

7. Write the vocabulary word that matches the definition. 4. An angle whose measure is more than 0° but less than 90° 5. the ray (or rays) that forms an angle 6. An angle whose measure is more than 90° but less than 180°

8. Write the vocabulary word that matches the definition. 7. Two non-adjacent angles formed by intersecting lines – on opposite sides of the vertex 8. A pair of rays that share a common endpoint 9. An angle whose measure is exactly 180° - in other words, a line!

9. A Naming Angles Angles can be named in up to four ways With the vertex letter With a number written in the angle’s interior With all three letters, written in either order, with the vertex letter in the middle C B 1 BB 11  ABC or  CBA

10. Name the angles below in four ways. 10. 11. A C R 8 D P I 2

11. Classifying Angles Angles can be classified based on the degree measurement, but without a protractor, you have to use your “common sense”. Angles that are bigger than an L shape are obtuse

12. Classifying Angles Angles that are smaller than an L shape are acute Without a protractor, a right angle can only be classified if it has a box at the vertex.

13. Classifying Angles A line is a straight angle … … if you label three points on it. JAN This one is called  JAN or  NAJ

14. Classify the angles as acute, right, obtuse, straight or impossible to tell. 12.13. 14.15.

15. Using Protractors The most important thing is to line up the protractor properly and to follow the correct “track” To pick the track, follow the ray out to the edge of the protractor and find the number 0 (or 10 on some protractors)

16. To measure this angle, line up a protractor pick the track follow the track 107 

17. 16. Measure the angle.

18. 17. Measure the angle.

19. Angle Bisectors An angle bisector is a ray that divides an angle into two congruent adjacent angles. X A O B m  AOX = m  XOB m  AOX = m  AOB 2 1 m  XOB = m  AOB 2 1 m  AOB = 2m  AOX m  AOB = 2m  XOB

20. Angle Bisectors If m  AOX = 7x + 18  and m  AOB = 24x + 6 , find x and the measure of each angle. X A O B m  AOB = 2m  AOX 24x + 6 = 2(7x + 18) 24x + 6 = 14x + 36 10x + 6 = 36 10x = 30 x = 3 m  AOX = 7(3) + 18 = 39  m  AOB = 24(3) + 6 = 78 

21. 18. If m  XOB = 9x + 52  and m  AOB = 18 – 25x , find x and the measure of each angle. 19. If m  XOA = 3x + 17  and m  BOX = 5x – 11 , find x and the measure of each angle.

22. Angle Addition Postulate The angle addition postulate says that for any pair of adjacent angles, the measure of the whole angle is equal to the sum of the measures of the two smaller adjacent angles. D A B C m  ABC = m  ABD + m  DBC

23. Angle Addition Postulate If m  ABC = 12x + 10 , m  ABD = 32  and m  DBC = 9x - 4 , find x and the measure of each angle. 12x + 10 = 32 + 9x - 4 m  ABC = m  ABD + m  DBC 12x + 10 = 28 + 9x 3x + 10 = 28 3x = 18 x = 6 m  ABC = 12(6) + 10 = 82  m  DBC = 9(6) – 4 = 50 

24. 20. If m  ABC = 7x + 6 , m  ABD = 3x – 4  and m  DBC = 70 , find x and the measure of each angle. 21. If m  ABC = 45 – 13x , m  ABD = 7x + 53  and m  DBC = 2x + 36 , find x and the measure of each angle.

25. Adjacent Angles Since adjacent angles can’t overlap, the side they share has to be the middle ray out of the three rays. A M H T The middle ray is HA so the adjacent angles are  MHA and  THA.

26. 22. Name the adjacent angles. S O C H

27. You’re finished! Show your paper to Ms. Jankowski or Mrs. Baldwin to get the answers! And don’t forget to study tonight!!!