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## EXAMPLE 2

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**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**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**Find the indicated measure in JKLM.**6. 3. 4. 5. NM m KML KM m JML 4 70° 40° 2 ANSWER ANSWER ANSWER ANSWER for Examples 2 and 3 GUIDED PRACTICE