Download Angles and Parallel Lines

NAME
DATE
3-2
PERIOD
Study Guide and Intervention
Angles and Parallel Lines
Parallel Lines and Angle Pairs
When two parallel lines are cut by a transversal,
the following pairs of angles are congruent.
• corresponding angles
• alternate interior angles
• alternate exterior angles
Also, consecutive interior angles are supplementary.
Example
In the figure, m∠2 = 75. Find the measures
of the remaining angles.
=
=
=
=
=
=
=
105
105
75
105
75
105
75
∠1
∠3
∠4
∠5
∠6
∠7
∠8
and
and
and
and
and
and
and
∠2
∠2
∠2
∠3
∠2
∠3
∠6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
In the figure, m∠3 = 102. Find the measure of each angle.
Tell which postulate(s) or theorem(s) you used.
102; Alt. Int. Angles Th.
1 2
4 3
m
5 6
8 7
n
p
Exercises
1. ∠5
p
form a linear pair.
form a linear pair.
are vertical angles.
are alternate interior angles.
are corresponding angles.
are corresponding angles.
are vertical angles.
2. ∠6 78; Cons. Int.
q
1 2
4 3
5 6
8 7
Lesson 3-2
m∠1
m∠3
m∠4
m∠5
m∠6
m∠7
m∠8
9 10
12 11
13 14
16 15
3. ∠11 102; Corre. Angles Th.
Angles Th.
4. ∠7 102; Corre. Angles Th.
5. ∠15 102; Corre. Angles Th.
6. ∠14 78; Cons. Int. Angles Th;
m
n
Corre. Angles Th.
In the figure, m∠9 = 80 and m∠5 = 68. Find the measure
of each angle. Tell which postulate(s) or theorem(s) you used.
7. ∠12 100; Supp. Angles
9. ∠4 100; Cons Int. Angles Th.
11. ∠7 68; Vertical Angles Th.
Chapter 3
8. ∠1 80;Corr. Angles
1 2
4 3
9 10
12 11
p
5 6
Th.
13 14
87
16 15
q
10. ∠3 80; Att. Int.
Angles Th.
w
v
12. ∠16 112; Vertical Angles Th; Cons.
Interior Angles Th.
11
Glencoe Geometry
NAME
DATE
3-2
PERIOD
Study Guide and Intervention
(continued)
Angles and Parallel Lines
Algebra and Angle Measures
Algebra can be used to find unknown values in
angles formed by a transversal and parallel lines.
Example
If m∠1 = 3x + 15, m∠2 = 4x - 5, and m∠3 = 5y,
find the value of x and y.
p q, so m∠1 = m∠2
because they are
corresponding angles.
m∠1 = m∠2
3x + 15 = 4x - 5
p
q
1
r s, so m∠2 = m∠3
because they are
corresponding angles.
2
4
r
3
s
m∠2 = m∠3
3x + 15 - 3x = 4x - 5 - 3x
15 = x - 5
15 + 5 = x - 5 + 5
75 = 5y
5y
5
75
−
=−
5
15 = y
20 = x
Exercises
Find the value of the variable(s) in each figure. Explain your reasoning.
2.
1.
(15x + 30)°
(3y + 18)°
10x°
(4x + 10)°
x = 15; y = 19; use corresponding
and supplementary angles
3.
(5y + 5)°
(11x + 4)°
x = 6; y = 24; Use consecutive
interior angles
4.
(13y - 5)°
5x°
2y°
3x°
4y°
x = 11; y = 10; use
consecutive interior angles
(5x - 20)°
x = 10; y = 25; Use consecutive
interior and alternate interior angles
Find the value of the variable(s) in each figure. Explain your reasoning.
5.
6.
2y°
(4z + 6)°
z°
2x° 90° x°
x°
106°
2y°
x = 30; y = 15 ; z = 150 use
supplementary, alternate interior,
and consecutive interior angles
x = 74; y = 37; z = 25;
use consecutive interior, corresponding,
and supplementary angles
Chapter 3
12
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
(5x - 5)°
(6y - 4)°
90°