Angle Addition Postulate

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Presentation transcript:

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

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

A B C D G K H J 134° 46° 46 Given: mÐGHK = 95 mÐGHJ = 114. Example 1: Example 2: Slide 3 G 114° K 46° 95° 19° H 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. mÐABD + mÐDBC = mÐABC mÐABD + mÐDBC = 180 So, if mÐABD = 134, then mÐDBC = ______ J Given: mÐGHK = 95 mÐGHJ = 114. Find: mÐKHJ. The Angle Addition Postulate tells us: mÐGHK + mÐKHJ = mÐGHJ 95 + mÐKHJ = 114 mÐKHJ = 19. Plug in what you know. 46 Solve.

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

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