Take note Theorem 6-4

Theorem

If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

If …

ABCD is a ▱ white parallelogram

Then …

m ∠ A + m ∠ B = 180 m angle , eh plus , m angle , b equals 180

m ∠ B + m ∠ C = 180 m angle , b plus , m angle , c equals 180

m ∠ C + m ∠ D = 180 m angle , c plus , m angle , d equals 180

m ∠ D + m ∠ A = 180 m angle , d plus , m angle , eh equals 180

You will prove Theorem 6-4 in Exercise 32.

Problem 1 Using Consecutive Angles

Multiple Choice What is m ∠ P m angle p in ▱ P Q R S white parallelogram p q r s ?

1. 26
2. 64
3. 116
4. 126

m ∠ P + m ∠ S = 180 Consecutive angles of a  ▱   are suppl . m ∠ P + 64 = 180 Substitute . m ∠ P = 116 Subtract 64 from each side . table with 3 rows and 3 columns , row1 column 1 , m angle p plus m angle s , column 2 equals180 , column 3 cap consecutiveanglesofa . white parallelogram . aresuppl . . , row2 column 1 , m angle p plus 64 , column 2 equals180 , column 3 cap substitute . . , row3 column 1 , m angle p , column 2 equals116 , column 3 cap subtract64fromeachside . . , end table

The correct answer is C.

✓ Got It?

1. Suppose you adjust the lamp so that m ∠ S = 86 . m angle , s equals 86 , . What is m ∠ R  in  ▱ P Q R S ? m angle r , in , white parallelogram p q r s question mark