Parallel Lines
Name:
1.
Date:
In the accompanying gure, what is one pair of alternate
interior angles?
3.
In the accompanying diagram, line ` is parallel to line m,
and line t is a transversal.
Which must be a true statement?
2.
A.
O1 and O2
B.
O4 and O5
C.
O4 and O6
D. O6 and O8
A.
mO1 + mO4 = 180
B.
mO1 + mO 8 = 180
C.
mO3 + mO6 = 180
D. mO2 + mO 5 = 180
4.
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In the accompanying diagram, transversal RS intersects
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parallel lines XY and WZ at E and H, respectively. If
mOHEY = 72, what is mOZHS ?
5.
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In the accompanying gure, parallel lines AB and CD are
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cut by transversal EF. If mOAEF = 40, nd mODFE.
In the accompanying diagram, lines a and b are parallel,
and lines c and d are transversals. Which angle is
congruent to angle 8?
A.
6
B.
5
C.
3
D. 4
page 1
6.
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In the accompanying diagram, AB is parallel to CD
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and transversal EF intersects AB and CD at G and H,
respectively. If mODHG : mOBGH = 1 : 2, nd mODHG.
7.
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In the accompanying diagram, parallel lines AB and CD
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are cut by transversal EF at R and S, respectively. If
mOERB = 72, nd mORSC.
8.
9.
10.
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In the accompanying diagram, AB, CD, EF, and GH are
straight lines. If mOw = 30, mOx = 30, and mOz = 120,
nd mOy.
11.
In the accompanying diagram, `1 k `2 k `3 . If mO1 = 70,
nd mO2.
12.
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In the accompanying diagram, RS k TU, and GH k MN. If
mOx = 115, nd mOy.
Parallel lines m and n are cut by transversal t. If
mO1 = 75, nd mO2.
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In the accompanying diagram, AB k CD, EF is a
transversal, and mO1 = 40. Find mO2.
page 2
Parallel Lines
13.
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.
16.
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In the accompanying diagram, parallel lines AB and CD
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are intersected by transversal EF at G and H, respectively.
If mOAGH = 4x + 30 and mOGHD = 7x 9, what is the
value of x ?
17.
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In the accompanying diagram, parallel lines AB and CD
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are intersected by transversal EF at G and H respectively.
If mOCHG = x + 20 and mODHG = 3x, nd the value
of x.
18.
In the accompanying diagram, parallel lines AB and CD
are intersected by transversal EF at G and H, respectively.
If mOBGH = 3x 5 and mOGHD = 6x + 14, what is the
value of x ?
What is the measure of the acute angle formed by Jay
Street and Main Street?
A.
14.
15.
45
B.
60
C.
90
D. 135
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In the accompanying diagram, AB is parallel to CD,
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and AB and CD are cut by transversal EF at points
G and H, respectively. If mOEGA = (2x + 30) and
mOEHC = (x + 80), nd x.
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In the accompanying diagram, parallel lines HE and AD
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are cut by transversal BF at points G and C, respectively.
If mOHGF = 5n and mOBCD = 2n + 66, nd n.
page 3
Parallel Lines
19.
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In the accompanying diagram, AB k CD. If mO1 = 4x
and mO2 = 2x 20, nd x.
20.
Two parallel lines are cut by a transversal. Two interior
angles on the same side of the transversal are represented
by 2x and 30 + x. What is the measure of the smaller
angle?
10
23.
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In the diagram below, transversal TU intersects PQ and RS
at V and W, respectively.
If mOTVQ = 5x 22 and mOVWS = 3x + 10, for which
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value of x is PQ k RS?
A.
21.
In the accompanying diagram, line a is parallel to
line b and line c is a transversal. If mO1 = 2x and
mO2 = 5x 54, what is the value of x?
24.
6
B.
16
C.
24
D. 28
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In the accompanying diagram, AB k CD, mOCAB = 80,
and mODCB = 40.
What is mOACB?
22.
As shown in the diagram below, lines m and n are cut by
transversal p.
A.
25.
40
B.
60
C.
80
D. 120
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In the accompanying diagram, AB is parallel to CD, AED
is a transversal, and CE is drawn. If mOCED = 60,
mODAB = 2x, and mODCE = 3x, nd x.
If mO1 = 4x + 14 and mO2 = 8x + 10, lines m and n are
parallel when x equals
A.
1
B.
6
C.
13
D. 17
page 4
Parallel Lines