1. EXAMPLE 2 Use properties of parallelograms So, m ADC + m BCD = 180°. Because m ADC = 110°, m BCD =180° –110° = 70°. SOLUTION By Theorem 8.5, the consecutive angle pairs in ABCD are supplementary. 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 BCD when m ADC = 110°.

2. EXAMPLE 3 Standardized Test Practice SOLUTION By Theorem 8.6, the diagonals of a parallelogram bisect each other. So, P is the midpoint of diagonals LN and OM. Use the Midpoint Formula. The correct answer is A. ANSWER = Coordinates of midpoint P of OM 4 + 0 2 7 + 0 2, ( ) = 7 2, 2 ( )

3. GUIDED PRACTICE for Examples 2 and 3 NM 3. SOLUTION By Theorem 8.6, the diagonals of a parallelogram bisect each other. So, N is the midpoint of diagonals KM. KN =NM Substitute 2 =NM Find the indicated measure in JKLM.

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

5. GUIDED PRACTICE for Examples 2 and 3 m JML 5. SOLUTION 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°. Find the indicated measure in JKLM.

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