1 4 Angle Addition Postulate First lets recall

1. 4 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: J K L 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…

1. 4 Angle Addition Postulate Slide 2 If B lies on the interior of ÐAOC, then mÐAOB + mÐBOC = mÐAOC. B A mÐAOC = 115° 50° O 65° C

Example 1: G D Example 2: 114° K 95° 19° H Given: mÐGHK = 95 mÐGHJ = 114. Find: mÐKHJ. J 134° A Slide 3 46° B C This is a special example, because the two adjacent angles together create a straight angle. Predict what mÐABD + mÐDBC equals. ÐABC is a straight angle, therefore mÐABC = 180. The Angle Addition Postulate tells us: mÐABD + mÐDBC = mÐABC mÐGHK + mÐKHJ = mÐGHJ 95 + mÐKHJ = 114 mÐKHJ = 19. Plug in what you know. Solve. mÐABD + mÐDBC = 180 So, if mÐABD = 134, 46 then mÐDBC = ______

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

B C mÐBQC = x – 7 mÐCQD = 2 x – 1 mÐBQD = 2 x + 34 Find x, mÐBQC, mÐCQD, mÐBQD. mÐBQC = x – 7 mÐBQC = 42 – 7 = 35 Q D mÐBQC + mÐCQD = mÐBQD x – 7 + 2 x – 1 = 2 x + 34 3 x – 8 = 2 x + 34 x – 8 = 34 x = 42 Algebra Connection Slide 5 mÐCQD = 2 x – 1 mÐCQD = 2(42) – 1 = 83 mÐBQD = 2 x + 34 mÐBQD = 2(42) + 34 = 118 Check: mÐBQC + mÐCQD = mÐBQD 35 + 83 = 118 x = 42 mÐCQD = 83 mÐBQC = 35 mÐBQD = 118