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Desk Lamp with Extending Arm: Parallelogram Angle Calculation

Learn how to calculate the angles of a desk lamp's extending arm, which forms a parallelogram, using Theorem 8.5 and 8.6. Examples and solutions provided.

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Desk Lamp with Extending Arm: Parallelogram Angle Calculation

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  1. Desk Lamp As shown, part of the extending arm of a desk lamp is a parallelogram. The angles of the parallelogram change as the lamp is raised and lowered. Find m BCDwhen m ADC = 110°. By Theorem 8.5, the consecutive angle pairs in ABCD are supplementary. So, m ADC + m BCD = 180°. Because m ADC = 110°, m BCD =180° –110° = 70°. EXAMPLE 2 Use properties of parallelograms SOLUTION

  2. By Theorem 8 .6, the diagonals of a parallelogram bisect each other. So, Pis the midpoint of diagonals LNand OM. Use the Midpoint Formula. 4 + 0 7 7 + 0 , , 2 Coordinates of midpoint Pof OM = ( ) ( ) = 2 2 2 ANSWER The correct answer is A. Standardized Test Practice EXAMPLE 3 SOLUTION

  3. Find the indicated measure in JKLM. 3. NM By Theorem 8 .6, the diagonals of a parallelogram bisect each other. So, Nis the midpoint of diagonals KM . KN = NM 2 = NM for Examples 2 and 3 GUIDED PRACTICE SOLUTION Substitute

  4. Find the indicated measure in JKLM. 4. KM KM = KN + NM KM = KM = for Examples 2 and 3 GUIDED PRACTICE SOLUTION By theorem 8.6 2 + 2 Substitute 4 Add

  5. Find the indicated measure in JKLM. 5. m JML By Theorem 8.5, the consecutive angle pairs in JKLM are supplementary. So, m KJM + m JML = 180°. Because m KJM = 110°, m JML =180° –110° = 70°. for Examples 2 and 3 GUIDED PRACTICE SOLUTION

  6. Find the indicated measure in JKLM. 6. m KML m JML = m KMJ + m KNL 30° + m KML m KML for Examples 2 and 3 GUIDED PRACTICE SOLUTION 70° = Substitute 40° = Subtract

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