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Parallel Lines 1
Teacher: Mr. Sime
Name: ____________________________________
1. 3. In the diagram, parallel lines transversal and are cut by
at R and S, respectively.
If m ∠ ERB = 72, find m ∠ RSC.
1. 18 3. 180
transversal and are intersected by
at G and H, respectively
If m ∠ CHG = x + 20 and m ∠ DHG = 3x, find the value of x.
1. 17.5 3. 50
2. 72 4. 108
2. 40
2. 4. 90
4. In the diagram, transversal and In the diagram, parallel lines intersects parallel lines , m ∠ DGH = x, and m ∠ BHG = 2x − 30.
In the diagram, parallel lines transversal and are intersected by
at G and H, respectively.
Find the value of x.
1. 30 3. 70
2. 50 4. 110
If m ∠ AGH = 4x + 30 and m ∠ GHD = 7x − 9, what is the
value of x?
1. 3 3. 13
2. 10 4. 18
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5. 7. In the diagram, line is parallel to line , m ∠ BAC =
46, and m ∠ BCD = 65.
Find the measure of ∠ ACB.
1. 11 3. 115
In the diagram, parallel lines transversal and are intersected by
at points G and H, respectively.
If m ∠ FGB = 2x + 25 and m ∠ FHD = 3x − 5, find x.
1. 20 3. 50
2. 30 4. 60
2. 69 4. 161
8. 6. In the diagram, In the diagram, transversal intersects parallel lines and at A and B, respectively.
intersects and is parallel to . Transversal at G and H, respectively.
If m ∠ AGH = 4x and m ∠ GHD = 3x + 40, what is the value of
x?
If m ∠ RAN = 3x + 24 and m ∠ RBQ = 7x − 16, find the value
of x.
1. 5
1. 20 3. 80
2. 40 4. 160
3. 10
2. 8.2 4. 16.4
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9. 11. In the diagram, transversal and intersects parallel lines at P and Q, respectively.
Figure 1
In the accompanying diagram of rectangle ABCD, m ∠ BAC =
3x + 4 and m ∠ ACD = x + 28. What is m ∠ CAD?
If m ∠ RPM = 50, find m ∠ PQU.
1. 12 3. 40
1. 40 3. 130
2. 37 4. 50
2. 50 4. 140
12. 10. In the diagram, parallel lines transversal and are cut by
at E and F, respectively.
If m ∠ GEB = (2x − 30) and m ∠ EFD = (x + 15), find the
value of x.
1. 25 3. 45
2. 35 4. 65
Figure 2
In the diagram, and . If m ∠ 1 = 68, what is
m ∠ 3?
1. 22 3. 90
2. 68 4. 112
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13. 15. Figure 5
Figure 3
In the diagram: Which statement is true?
In the diagram, , , , and are straight lines. If
m ∠ w = 30, m ∠ x = 30, and m ∠ z = 120, find m ∠ y.
1. ∠ w ≅ ∠ y
1. 15 3. 60
3. ∠ w ≅ ∠ z
2. 30 4. 110
and bisects ∠ CFB.
2. ∠ y ≅ ∠ z
4. ∠ x ≅ ∠ y 16. 14. Figure 4
In the diagram, parallel lines l and m are cut by transversal t. Which statement about angles 1 and 2 must be true?
1. ∠ 1 ≅ ∠ 2
2. ∠ 1 is a complement to ∠ 2.
3. ∠ 1 is a supplement to ∠ 2.
4. ∠ 1 and ∠ 2 are right angles. http://www.castlelearning.com/review/teacher/AssignmentPrinting.aspx
Figure 6
In the diagram: ≅ , ∠ D ≅ ∠ B, and || . Is ?
1. yes
2. no
3. cannot tell
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17. 19. Figure 7
In the diagram, l1 || l2 || l3 . If m ∠ 1 =70, find m ∠ 2.
1. 20 3. 100
2. 70 4. 110
Figure 9
In the diagram: and is a transversal. If
m ∠ JLB = 6x ­ 7 and m ∠ LJD = 7x + 5, what is the value of
x?
1. ­2 3. 7
18. 2. 6 4. 14
20. Figure 8
In the diagram, and is a transversal. If
m ∠ AEF = 2x + 40 and m ∠ EFD = 3x + 10, find x.
Figure 10
1. 10 3. 30
In the diagram: 2. 20 4. 50
and C is the midpoint of ≅ ΔEDC ?
, , and , ∠ A ≅ ∠ E,
. Which theorem justifies ΔABC
1. SSS ≅ SSS 3. ASA ≅ ASA
2. SAS ≅ SAS 4. SSA ≅ SSA
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21. 23. Figure 13
Figure 11
In the diagram: Parallel lines and are cut by
transversal at P and Q, respectively. Which statement
must always be true?
In the diagram, parallel lines
and are intersected by at E and F, respectively. If m ∠ BEF = 5x − 10 and
m ∠ CFE = 4x + 20, find x.
1. m ∠ APE = m ∠ CQF
1. 9 3. 25
2. m ∠ APE < m ∠ CQF
2. 18 4. 30
3. m ∠ APE + m ∠ CQF = 90
4. m ∠ APE + m ∠ CQF = 180
24. 22. Figure 14
Figure 12
In the diagram: , m ∠ AGF = 30, and m ∠ CEF
= 45. What is m ∠ GFE ?
1. 45 3. 60
2. 52 4. 75
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In the diagram, ||
, is a transversal, and is
drawn. If m ∠ CED = 60, m ∠ DAB = 2x, and m ∠ DCE = 3x,
find x.
1. 16 3. 30
2. 24 4. 66
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25. 27. Figure 17
Figure 15
In the diagram, parallel lines l and m are cut by transversal t.
Which statement is true?
1. m ∠ 1 + m ∠ 2 + m ∠ 5 = 360
2. m ∠ 1 + m ∠ 2 + m ∠ 3 = 180
3. m ∠ 1 + m ∠ 2 = m ∠ 2 + m ∠ 3
4. m ∠ 1 + m ∠ 3 = m ∠ 4 + m ∠ 5
In the diagram, ||
, m ∠ x = 50, and m ∠ y = 60. What
is m ∠ z?
1. 70 3. 100
2. 80 4. 110
28. In the accompanying diagram, parallel lines intersected by transversal = 123. 26. and are
at points X and Y, and m ∠ FYD
Figure 16
In the diagram, line l is parallel to line m and line t is a
transversal. If m ∠ 1 = 2x + 20 and m ∠ 2 = 4x + 10, what is
m ∠ AXY = the number of degrees in ∠ 3?
1. 25 3. 70
2. 40 4. 110
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29. 31. In the accompanying diagram, , , , ,
, and m ∠ CAB = m ∠ FDE
In the accompanying figure, what is one pair of alternate
interior angles?
= 90.
Which statement would not be used to prove ΔABC ≅ ΔDEF?
1. SSS ≅ SSS 3. AAS ≅ AAS
1. ∠ 1 and ∠ 2
2. SAS ≅ SAS 4. HL ≅ HL
2. ∠ 4 and ∠ 5
3. ∠ 4 and ∠ 6
30. 4. ∠ 6 and ∠ 8
Two parallel roads, Elm Street and Oak Street, are crossed by a
third, Walnut Street, as shown in the accompanying diagram. 32. In the accompanying diagram, line m is parallel to line p, line
t is a transversal, m ∠ a = 3x + 12, and m ∠ b = 2x + 13. Find
the value of x.
Find the number of degrees in the acute angle formed by the
intersection of Walnut Street and Elm Street.
Answer: °
x = http://www.castlelearning.com/review/teacher/AssignmentPrinting.aspx
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33. In the accompanying diagram, parallel lines 35. and are
intersected by transversal at points G and H,
respectively, m ∠ AGH= x + 15, and m ∠ GHD = 2x.
In the accompanying diagram, lines a and b are parallel, and
lines c and d are transversals.
Which angle is congruent to angle 8?
1. 6 3. 3
Which equation can be used to find the value of x?
1. 2x = x + 15
2. 2x + x + 15 = 180
3. 2x + x + 15 = 90
4. 2x(x + 15) = 0
34. The accompanying diagram shows a football player crossing
the 20­yard line at an angle of 30° and continuing along the
same path.
What is the measure of angle B, where the player crosses into
the end zone?
2. 5 4. 4
36. The accompanying diagram shows two parallel streets, Main
Street and Brooks Road, intersected by Jay Street. The obtuse
angle that Jay Street forms with Brooks Road is three times
the measure of the acute angle that Jay Street forms with Main
Street.
What is the measure of the acute angle formed by Jay Street
and Main Street?
1. 45° 3. 90°
1. 30° 3. 150°
2. 60° 4. 135°
2. 60° 4. 180°
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37. 39. In the accompanying diagram, In the accompanying diagram, line is parallel to line m,
and line t is a transversal.
, is a
transversal, m ∠ DGH = 2x, and m ∠ FHB = 5x ­ 51. Which must be a true statement?
1. m ∠ 1 + m ∠ 4 = 180
2. m ∠ 1 + m ∠ 8 = 180
3. m ∠ 3 + m ∠ 6 = 180
4. m ∠ 2 + m ∠ 5 = 180
40. Find the measure, in degrees, of ∠ BHE.
Answer: The accompanying diagram shows two parallel roads, Hope
Street and Grand Street, crossed by a transversal road,
Broadway.
°
38. In the accompanying diagram, , transversals and H and I, respectively.
. From point E on are drawn, intersecting at
If m ∠ 1 = 110, what is the measure of ∠ 7?
1. 40° 3. 110°
If m ∠ CHF = 20 and m ∠ DIG = 60, what is m ∠ HEI?
2. 70° 4. 180°
1. 60 3. 100
2. 80 4. 120
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