Angle Addition Postulate and examples.

1. Angle Addition Postulate First, let’s recall some previous information from last week…. We discussed the Segment Addition Postulate , which stated that we could add the lengths of adjacent segments together to get the length of an entire segment. For example: JK + KL = JL If you know that JK = 7 and KL = 4, then you can conclude that JL = 11. The Angle Addition Postulate is very similar, yet applies to angles. It allows us to add the measures of adjacent angles together to find the measure of a bigger angle… J K L

2. Angle Addition Postulate A B C O If B lies on the interior of  AOC, then m  AOB + m  BOC = m  AOC. m  AOC = 115  50  65 

3. Examples: This is a special example, because the two adjacent angles together create a straight angle. Predict what m  ABD + m  DBC equals.  ABC is a straight angle, therefore m  ABC = 180. m  ABD + m  DBC = m  ABC m  ABD + m  DBC = 180 So, if m  ABD = 134, then m  DBC = ______ 46 G H J K Given: m  GHK = 95 m  GHJ = 114 . Find: m  KHJ . The Angle Addition Postulate tells us: m  GHK + m  KHJ = m  GHJ 95 + m  KHJ = 114 m  KHJ = 19. 19  Plug in what you know. Solve. 46 ° A B C D 134° 95  114 

4. Algebra Connection R S T V Given: m  RSV = x + 5 m  VST = 3x - 9 m  RST = 68 Find x. m  RSV + m  VST = m  RST x + 5 + 3x – 9 = 68 4x- 4 = 68 4x = 72 x = 18 Set up an equation using the Angle Addition Postulate. Plug in what you know. Solve. Extension : Now that you know x = 18, find m  RSV and m  VST. m  RSV = x + 5 m  RSV = 18 + 5 = 23 m  VST = 3x - 9 m  VST = 3(18) – 9 = 45 Check: m  RSV + m  VST = m  RST 23 + 45 = 68

5. Algebra Connection B Q D C m  BQC = x – 7 m  CQD = 2x – 1 m  BQD = 2x + 34 Find x, m  BQC , m  CQD , m  BQD . m  BQC + m  CQD = m  BQD 3x – 8 = 2x + 34 x – 7 + 2x – 1 = 2x + 34 x – 8 = 34 x = 42 m  BQC = x – 7 m  BQC = 42 – 7 = 35 m  CQD = 2x – 1 m  CQD = 2(42) – 1 = 83 m  BQD = 2x + 34 m  BQD = 2(42) + 34 = 118 Check: m  BQC + m  CQD = m  BQD 35 + 83 = 118 x = 42 m  BQC = 35 m  CQD = 83 m  BQD = 118