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Understanding Angle Measures and Relationships in Geometry

This lesson covers the measurement and relationships between angles in geometry, focusing on naming conventions and properties. Key concepts include measuring angles, the relationships of complementary and supplementary angles, and the significance of opposite angles. You will learn how to calculate specific angle measures using algebraic expressions and validate solutions. Examples such as m∠ABD, m∠PQR, and m∠GHI provide practical applications. Collaborate with a partner to summarize and discuss key points to reinforce your understanding of these concepts.

hilary-finch
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Understanding Angle Measures and Relationships in Geometry

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  1. mSQR mPQS mPQR Note, we have to use 3 letters to uniquely identify each angle. “measure of angle” “cut into equal halves” ½  mDEF mFEW mDEW mFEW mDEF mDEW add to 90 right angle “corner angles” mMLW = 90 mKLW + add to 180 straight line mJHW = 180 mGHW + two lines intersect congruent (equal measure) opposite mPWS mRWQ mPWQ mRWS

  2. Now plug in … mABD = 2(8) + 26 mABD = 42 mCBD= 6(8) mCBD= 48 2x + 26 6x 2x + 26 + 6x = 90 8x + 26 = 90 x = 8 Check: 42 + 48 90  127 Now plug in … mPQS = 43 + 3 mPQS = 46 mSQR = 2(43) – 5 mSQR = 81 x + 3 2x – 5 x + 3 + 2x – 5 = 127 3x – 2 = 127 x = 43 Check: 46 + 81 127  Now plug in … mGHI = 5(23) – 1 mGHI = 114 3x – 3 5x – 1 3x – 3 + 5x – 1 = 180 8x – 4 = 180 x = 23 mFHG= 3(23) – 3 mFHG= 66

  3. 88 44 Be Careful here! P P P T T T x + 11 = ½  88 x + 11 = 44 x = 33 44 (x + 11) Q Q Q R R R 10x – 7 ??? 4x + 6 + 5x = 10x – 7 9x + 6 = 10x – 7 x = 13 6x + 1 4x + 6 5x mPQR = 10(13) – 7 mPQR = 123 10x – 13 6x + 1 = 10x – 13 14 = 4x x = 3.5 mPQR = 6x + 1 + 10x – 13 mPQR = 16x – 12 mPQR = 16(3.5) – 12 mPQR = 56 – 12 = 44

  4. Lesson Summary! Quietly review your notes. Add a short paragraph summarizing the key points of today’s lesson. When you and your assigned class partner are finished, discuss your summary with your partner and add things you missed. Be prepared to share your summary with the class.

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