3. To measure angles using a protractor. To draw angles using a protractor. Different types of angles

4. In geometry, angles are measured in units called _______. degrees The symbol for degree is °. Q P R 75° In the figure below, the angle is 75 degrees.

5. Now, let’s measure an angle using a protractor. Q R S Use a protractor to measure SRQ. 1) Place the center point of the protractor on vertex R. Align the straightedge with side RS. 2) Use the scale that begins with 0 at RS. Read where the other side of the angle, RQ, crosses this scale. 120 0

6. J H G S Q R m SRQ = Find the measurement of: m SRJ = m SRG = 180 45 150 Let’s measure the following angles.

7. J H G S Q R m QRG = m GRJ = 70 180 – 150 = 30 150 – 45 = 105 m SRH Let’s measure an angles

8. Use a protractor to draw an angle having a measure of 135. 1) Draw AB 2) Place the center point of the protractor on A. Align the mark labeled 0 with the ray. 3) Locate and draw point C at the mark labeled 135. Draw AC. C A B Try this one.

9. acute angle: less than 90 0 Lets look at some angles. right angle: 90 0 obtuse angle: more than 90 0 straight angle: 180 0

10. Classify each angle as acute, obtuse, or right. 110° 90° 40° 50° 130° 75° Obtuse Obtuse Acute Acute Acute Right

11. 5x - 7 B The measure of B is 138. Solve for x. B = 5x – 7 and B = 138 Given: (What do you know?) 5x – 7 = 138 5x = 145 x = 29 5(29) -7 = ? 145 -7 = ? 138 = 138 Check! Let’s use Algebra to answer the following.

12. Here’s another one. 9y + 4 H The measure of H is 67. Solve for y. H = 9y + 4 and H = 67 Given: (What do you know?) 9y + 4 = 67 9y = 63 y = 7 9(7) + 4 = ? 63 + 4 = ? 67 = 67 Check!

13. Is m a larger than m b ? 60°

14. 1) Draw an acute, an obtuse, or a right angle. Label the angle RST. R T S 2) Draw and label a point X in the interior of the angle. Then draw SX. X 3) For each angle, find m  RSX, m  XST, and  RST. 30° 45° 75° Let’s try something different.

15. congruent angles: Here are some more types of angles. vertical angles: opposite angles adjacent angles:

16. Determine whether  1 and  2 are adjacent angles. No. They have a common vertex B, but _____________ no common side 1 2 B 1 2 G Yes. They have the same vertex G and a common side with no interior points in common. N 1 2 J L No. They do not have a common vertex or ____________ a common side The side of  1 is ____ The side of  2 is ____ Here are some questions.

17. Determine whether  1 and  2 are adjacent angles. No. 2 1 Yes. 1 2 X D Z In this example, the noncommon sides of the adjacent angles form a ___________. straight line These angles are called a _________ linear pair Let’s try something different.

18. Find the value of x in the figure: The angles are vertical angles. So, the value of x is 130°. 130° x° Let’s try something different.

19. Find the value of x in the figure: The angles are vertical angles. (x – 10) = 125. (x – 10)° 125° x – 10 = 125. x = 135. Let’s try something different.

20. Assignment

21. 1.6 Measuring Angles Geometry 5. If m  1 = 2x + 3 and the m  3 = 3x + 2, then find the m  3 6. If m  ABD = 4x + 5 and the m  DBC = 2x + 1, then find the m  EBC 7. If m  1 = 4x - 13 and the m  3 = 2x + 19, then find the m  4 8. If m  EBG = 7x + 11 and the m  EBH = 2x + 7, then find the m  1 A B C D E G H 1 2 3 4 Draw the following angles. 1. 50 0 2. 75 0 3. 135 0 4. 115 0