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To measure angles using a protractor. To draw angles using a protractor. Different types of angles In geometry, angles are measured in units called degrees _______. The symbol for degree is °. In the figure below, the angle is 75 degrees. P Q 75° R Now, let’s measure an angle using a protractor. 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. Q 1200 R S Let’s measure the following angles. Find the measurement of: m SRQ = 180 m SRJ = 45 m SRG = 150 H J G Q R S Let’s measure an angles m SRH 70 m QRG = 180 – 150 = 30 m GRJ = 150 – 45 = 105 H J G Q R S Try this one. Use a protractor to draw an angle having a measure of 135. 1) Draw AB 3) Locate and draw point C at the mark labeled 135. Draw AC. 2) Place the center point of the protractor on A. Align the mark labeled 0 with the ray. C A B Lets look at some angles. acute angle: less than 900 obtuse angle: more than 900 right angle: 900 straight angle: 1800 Classify each angle as acute, obtuse, or right. 110° 40° 90° Obtuse Right Acute 50° 130° Acute Obtuse 75° Acute Let’s use Algebra to answer the following. The measure of Solve for x. B is 138. 5x - 7 B Given: (What do you know?) B = 5x – 7 and 5x – 7 = 138 5x = 145 x = 29 B = 138 Check! 5(29) -7 = ? 145 -7 = ? 138 = 138 Here’s another one. The measure of Solve for y. H is 67. H 9y + 4 Given: (What do you know?) H = 9y + 4 and 9y + 4 = 67 9y = 63 y=7 H = 67 Check! 9(7) + 4 = ? 63 + 4 = ? 67 = 67 Is m a a larger than m 60° b? b 60° Let’s try something different. 1) Draw an acute, an obtuse, or a right angle. Label the angle RST. R 45° 2) Draw and label a point X in the interior of the angle. Then draw SX. X 75° S 3) For each angle, find mRSX, mXST, and RST. 30° T Here are some more types of angles. congruent angles: vertical angles: opposite angles adjacent angles: Here are some questions. Determine whether 1 and 2 are adjacent angles. No. They have a common vertex B, but no common side _____________ 2 1 B 1 Yes. They have the same vertex G and a common side with no interior points in common. 2 G N L J 2 1 No. They do not have a common vertex or a common side ____________ LN The side of 1 is ____ JN The side of 2 is ____ Let’s try something different. Determine whether 1 and 2 are adjacent angles. No. 1 2 Yes. 1 X 2 D Z In this example, the noncommon sides of the adjacent angles form a straight line ___________. linear pair These angles are called a _________ Let’s try something different. Find the value of x in the figure: 130° x° The angles are vertical angles. So, the value of x is 130°. Let’s try something different. Find the value of x in the figure: (x – 10)° 125° The angles are vertical angles. (x – 10) = 125. x – 10 = 125. x = 135. Assignment 1.6 Measuring Angles Geometry Draw the following angles. 1. 500 2. 750 3. 1350 4. 1150 G 5. If m1 = 2x + 3 and the m3 = 3x + 2, then find the m3 D 1 6. If mABD = 4x + 5 and the mDBC = 2x + 1, then find the mEBC A 4 7. If m1 = 4x - 13 and the m3 = 2x + 19, then find the m4 3 B E 8. If mEBG = 7x + 11 and the mEBH = 2x + 7, then find the m1 H 2 C ???