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°.

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 + 02

7 + 02

,( ) = 72

,2 ( )

GUIDED PRACTICE for Examples 2 and 3

NM3.

SOLUTION

By Theorem 8 .6, the diagonals of a parallelogram bisect each other. So, N is the midpoint of diagonals KM .

KN = NM

Substitute2 = NM

Find the indicated measure in JKLM.

GUIDED PRACTICE for Examples 2 and 3

Find the indicated measure in JKLM.

KM 4.

SOLUTION

By theorem 8.6KM = KN + NM

SubstituteKM = 2 + 2

AddKM = 4

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.

GUIDED PRACTICE for Examples 2 and 3

Find the indicated measure in JKLM.

m KML 6.

SOLUTION

m JML = m KMJ + m KNL

Substitute70° = 30° + m KML

Subtract40° = m KML