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3-2 Assignment.Find each angle measure. 1. m1 2. mABC 3. mDEF
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LESSON
x-x
3-123-12
LESSON
3-2
CS10_G_MECR710617_C03L02b.indd 12 4/8/11 9:58:02 AM
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LESSON
x-x
3-123-12
LESSON
3-2
CS10_G_MECR710617_C03L02b.indd 12 4/8/11 9:58:02 AM
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LESSON
x-x
3-123-12
LESSON
3-2
CS10_G_MECR710617_C03L02b.indd 12 4/8/11 9:58:02 AM
4. Ocean waves move in parallel lines toward the shore. The figure shows Sandy Beaches windsurfing across several waves. For this exercise, think of Sandy’s wake as a line. m∠1 = (2x + 2y)° and m∠2 = (2x + y)°. Find x and y. x = _________ y = _________
Name________________________________________ Date__________________ Class__________________
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LESSON
x-x
3-123-12
LESSON
3-2
CS10_G_MECR710617_C03L02b.indd 12 4/8/11 9:58:02 AM
Use the diagram of a staircase railing. AG ||CJ and AD || FJ . Choose the best answer.
5. _____ Which is a true statement about the measure of ∠DCJ? A It equals 30°, by the Alternate Interior Angles Theorem. B It equals 30°, by the Corresponding Angles Postulate. C It equals 50°, by the Alternate Interior Angles Theorem. D It equals 50°, by the Corresponding Angles Postulate.
6. _____ Which is a true statement about the value of n? F It equals 25°, by the Alternate Interior Angles Theorem. G It equals 25°, by the Same-Side Interior Angles Theorem. H It equals 35°, by the Alternate Interior Angles Theorem. J It equals 35°, by the Same-Side Interior Angles Theorem.
7. In the diagram, which represents the side view of a mystery spot,
mSRT = 25°, RT
is a transversal to
PS &QR .
a) What type of angle pair is QRT & STR?
b) Find mSTR. Use a postulate or theorem to justify your answer
Name________________________________________ Date__________________ Class__________________
30. Land Development A piece of property
2
1lies between two parallel streets as shown. m!1 = (2x + 6) °, and m!2 = (3x + 9) °. What is the relationship between the angles? What are their measures?
31. /////ERROR ANALYSIS///// In the figure, AD
BC
m!ABC = (15x + 5) °, and m!BCD = (10x + 25) °. Which value of m!BCD is incorrect? Explain.
A B
m!BCD = 10(4) + 25 = 65˚
- -
+ =- -
+ = +
=
=
+ + + =
m!BCD = 10(6) + 25 = 85˚
=
=
+ =
- -
32. Critical Thinking In the diagram, ! " m.
m
x˚
x˚
y˚!Explain why x _ y = 1.
33. Write About It Suppose that lines ! and m are intersected by transversal p. One of the angles formed by ! and p is congruent to every angle formed by m and p. Draw a diagram showing lines !, m, and p, mark any congruent angles that are formed, and explain what you know is true.
34. m!RST = (x + 50) °, and m!STU = (3x + 20) °. R
V T U
S Find m!RVT.
15° 65° 27.5° 77.5°
29. In the diagram, which represents the side view of P
S
Q
RT
a mystery spot, m!SRT = 25°. # $% RT is a transversal
to # $% PS and # $% QR .
a. What type of angle pair is !QRT and !STR?
b. Find m!STR. Use a theorem or postulate to justify your answer.
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© R
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160 Chapter 3 Parallel and Perpendicular Lines
CS10_G_MESE612294_C03L02.indd 160CS10_G_MESE612294_C03L02.indd 160 2/20/11 2:41:21 AM2/20/11 2:41:21 AM
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LESSON
x-x
3-173-17
LESSON
3-2
CS10_G_MECR710617_C03L02f.indd 17 4/8/11 9:56:41 AM
8.
30. Land Development A piece of property
2
1lies between two parallel streets as shown. m!1 = (2x + 6) °, and m!2 = (3x + 9) °. What is the relationship between the angles? What are their measures?
31. /////ERROR ANALYSIS///// In the figure, AD
BC
m!ABC = (15x + 5) °, and m!BCD = (10x + 25) °. Which value of m!BCD is incorrect? Explain.
A B
m!BCD = 10(4) + 25 = 65˚
- -
+ =- -
+ = +
=
=
+ + + =
m!BCD = 10(6) + 25 = 85˚
=
=
+ =
- -
32. Critical Thinking In the diagram, ! " m.
m
x˚
x˚
y˚!Explain why x _ y = 1.
33. Write About It Suppose that lines ! and m are intersected by transversal p. One of the angles formed by ! and p is congruent to every angle formed by m and p. Draw a diagram showing lines !, m, and p, mark any congruent angles that are formed, and explain what you know is true.
34. m!RST = (x + 50) °, and m!STU = (3x + 20) °. R
V T U
S Find m!RVT.
15° 65° 27.5° 77.5°
29. In the diagram, which represents the side view of P
S
Q
RT
a mystery spot, m!SRT = 25°. # $% RT is a transversal
to # $% PS and # $% QR .
a. What type of angle pair is !QRT and !STR?
b. Find m!STR. Use a theorem or postulate to justify your answer.
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© R
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Dav
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and
Fun
Ent
husi
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160 Chapter 3 Parallel and Perpendicular Lines
CS10_G_MESE612294_C03L02.indd 160CS10_G_MESE612294_C03L02.indd 160 2/20/11 2:41:21 AM2/20/11 2:41:21 AM
9. In the diagram, || m,Explain why xy= 1.
10. Suppose that lines ℓ and m are intersected by transversal p. One of the angles formed by ℓ and p is congruent to every angle formed by m and p. Draw a diagram showing lines ℓ, m, and p, mark any congruent angles that are formed, and explain what you know is true.
30. Land Development A piece of property
2
1lies between two parallel streets as shown. m!1 = (2x + 6) °, and m!2 = (3x + 9) °. What is the relationship between the angles? What are their measures?
31. /////ERROR ANALYSIS///// In the figure, AD
BC
m!ABC = (15x + 5) °, and m!BCD = (10x + 25) °. Which value of m!BCD is incorrect? Explain.
A B
m!BCD = 10(4) + 25 = 65˚
- -
+ =- -
+ = +
=
=
+ + + =
m!BCD = 10(6) + 25 = 85˚
=
=
+ =
- -
32. Critical Thinking In the diagram, ! " m.
m
x˚
x˚
y˚!Explain why x _ y = 1.
33. Write About It Suppose that lines ! and m are intersected by transversal p. One of the angles formed by ! and p is congruent to every angle formed by m and p. Draw a diagram showing lines !, m, and p, mark any congruent angles that are formed, and explain what you know is true.
34. m!RST = (x + 50) °, and m!STU = (3x + 20) °. R
V T U
S Find m!RVT.
15° 65° 27.5° 77.5°
29. In the diagram, which represents the side view of P
S
Q
RT
a mystery spot, m!SRT = 25°. # $% RT is a transversal
to # $% PS and # $% QR .
a. What type of angle pair is !QRT and !STR?
b. Find m!STR. Use a theorem or postulate to justify your answer.
© R
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and
Fun
Ent
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© R
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Dav
is/D
arkh
ouse
and
Fun
Ent
husi
ast
160 Chapter 3 Parallel and Perpendicular Lines
CS10_G_MESE612294_C03L02.indd 160CS10_G_MESE612294_C03L02.indd 160 2/20/11 2:41:21 AM2/20/11 2:41:21 AM
Name________________________________________ Date__________________ Class__________________
30. Land Development A piece of property
2
1lies between two parallel streets as shown. m!1 = (2x + 6) °, and m!2 = (3x + 9) °. What is the relationship between the angles? What are their measures?
31. /////ERROR ANALYSIS///// In the figure, AD
BC
m!ABC = (15x + 5) °, and m!BCD = (10x + 25) °. Which value of m!BCD is incorrect? Explain.
A B
m!BCD = 10(4) + 25 = 65˚
- -
+ =- -
+ = +
=
=
+ + + =
m!BCD = 10(6) + 25 = 85˚
=
=
+ =
- -
32. Critical Thinking In the diagram, ! " m.
m
x˚
x˚
y˚!Explain why x _ y = 1.
33. Write About It Suppose that lines ! and m are intersected by transversal p. One of the angles formed by ! and p is congruent to every angle formed by m and p. Draw a diagram showing lines !, m, and p, mark any congruent angles that are formed, and explain what you know is true.
34. m!RST = (x + 50) °, and m!STU = (3x + 20) °. R
V T U
S Find m!RVT.
15° 65° 27.5° 77.5°
29. In the diagram, which represents the side view of P
S
Q
RT
a mystery spot, m!SRT = 25°. # $% RT is a transversal
to # $% PS and # $% QR .
a. What type of angle pair is !QRT and !STR?
b. Find m!STR. Use a theorem or postulate to justify your answer.
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and
Fun
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© R
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Dav
is/D
arkh
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and
Fun
Ent
husi
ast
160 Chapter 3 Parallel and Perpendicular Lines
CS10_G_MESE612294_C03L02.indd 160CS10_G_MESE612294_C03L02.indd 160 2/20/11 2:41:21 AM2/20/11 2:41:21 AM
30. Land Development A piece of property
2
1lies between two parallel streets as shown. m!1 = (2x + 6) °, and m!2 = (3x + 9) °. What is the relationship between the angles? What are their measures?
31. /////ERROR ANALYSIS///// In the figure, AD
BC
m!ABC = (15x + 5) °, and m!BCD = (10x + 25) °. Which value of m!BCD is incorrect? Explain.
A B
m!BCD = 10(4) + 25 = 65˚
- -
+ =- -
+ = +
=
=
+ + + =
m!BCD = 10(6) + 25 = 85˚
=
=
+ =
- -
32. Critical Thinking In the diagram, ! " m.
m
x˚
x˚
y˚!Explain why x _ y = 1.
33. Write About It Suppose that lines ! and m are intersected by transversal p. One of the angles formed by ! and p is congruent to every angle formed by m and p. Draw a diagram showing lines !, m, and p, mark any congruent angles that are formed, and explain what you know is true.
34. m!RST = (x + 50) °, and m!STU = (3x + 20) °. R
V T U
S Find m!RVT.
15° 65° 27.5° 77.5°
29. In the diagram, which represents the side view of P
S
Q
RT
a mystery spot, m!SRT = 25°. # $% RT is a transversal
to # $% PS and # $% QR .
a. What type of angle pair is !QRT and !STR?
b. Find m!STR. Use a theorem or postulate to justify your answer.
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and
Fun
Ent
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© R
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Dav
is/D
arkh
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and
Fun
Ent
husi
ast
160 Chapter 3 Parallel and Perpendicular Lines
CS10_G_MESE612294_C03L02.indd 160CS10_G_MESE612294_C03L02.indd 160 2/20/11 2:41:21 AM2/20/11 2:41:21 AM
Find m∠1 in each diagram. (Hint: Draw a line parallel to the given parallel lines.) 11. 12.
35. For two parallel lines and a transversal, m!1 = 83°. For which pair of angle measures is the sum the least?
!1 and a corresponding angle !1 and a same-side interior angle !1 and its supplement !1 and its complement
36. Short Response Given a " b with transversal t,
a b
t
1 2
3explain why !1 and !3 are supplementary.
CHALLENGE AND EXTENDMulti-Step Find m!1 in each diagram. (Hint: Draw a line parallel to the given parallel lines.)
37.
1
145˚
40˚
38. 1
105˚
80˚
39. Find x and y in the diagram. Justify your answer.
40. Two lines are parallel. The measures
m
n
pq
72˚
(10x + 5y)˚
(15x + 4y)˚80˚
of two corresponding angles are a° and 2b°, and the measures of two same-side interior angles are a° and b°. Find the value of a.
3-2 Angles Formed by Parallel Lines and Transversals 161
CS10_G_MESE612294_C03L02.indd 161CS10_G_MESE612294_C03L02.indd 161 2/20/11 2:41:23 AM2/20/11 2:41:23 AM
35. For two parallel lines and a transversal, m!1 = 83°. For which pair of angle measures is the sum the least?
!1 and a corresponding angle !1 and a same-side interior angle !1 and its supplement !1 and its complement
36. Short Response Given a " b with transversal t,
a b
t
1 2
3explain why !1 and !3 are supplementary.
CHALLENGE AND EXTENDMulti-Step Find m!1 in each diagram. (Hint: Draw a line parallel to the given parallel lines.)
37.
1
145˚
40˚
38. 1
105˚
80˚
39. Find x and y in the diagram. Justify your answer.
40. Two lines are parallel. The measures
m
n
pq
72˚
(10x + 5y)˚
(15x + 4y)˚80˚
of two corresponding angles are a° and 2b°, and the measures of two same-side interior angles are a° and b°. Find the value of a.
3-2 Angles Formed by Parallel Lines and Transversals 161
CS10_G_MESE612294_C03L02.indd 161CS10_G_MESE612294_C03L02.indd 161 2/20/11 2:41:23 AM2/20/11 2:41:23 AM
13. Find x and y in the diagram. Justify your answer.
14. Two lines are parallel. The measures of two corresponding angles are a° and 2b°, and the measures of two same-side interior angles are a° and b°. Find the value of a.
Name________________________________________ Date__________________ Class__________________
35. For two parallel lines and a transversal, m!1 = 83°. For which pair of angle measures is the sum the least?
!1 and a corresponding angle !1 and a same-side interior angle !1 and its supplement !1 and its complement
36. Short Response Given a " b with transversal t,
a b
t
1 2
3explain why !1 and !3 are supplementary.
CHALLENGE AND EXTENDMulti-Step Find m!1 in each diagram. (Hint: Draw a line parallel to the given parallel lines.)
37.
1
145˚
40˚
38. 1
105˚
80˚
39. Find x and y in the diagram. Justify your answer.
40. Two lines are parallel. The measures
m
n
pq
72˚
(10x + 5y)˚
(15x + 4y)˚80˚
of two corresponding angles are a° and 2b°, and the measures of two same-side interior angles are a° and b°. Find the value of a.
3-2 Angles Formed by Parallel Lines and Transversals 161
CS10_G_MESE612294_C03L02.indd 161CS10_G_MESE612294_C03L02.indd 161 2/20/11 2:41:23 AM2/20/11 2:41:23 AM