To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free)

Parallel Lines and Transversals Worksheet

Parallel Lines and Transversals Worksheet
  • Page 1
 1.  
The lines j and k are parallel. Find the values of x and y in the figure shown.


a.
x = 36 and y = 72
b.
x = 36 and y = 108
c.
x = 72 and y = 36
d.
x = 72 and y = 108


Solution:

2x° + 3x° = 180°
[Adjacent angles.]

5x° = 180°

x° = 180° / 5 = 36°

If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
[Corresponding angles postulate .]

y = (2x)
[From step 4.]

y = 2(36) = 72

So, x = 36 and y = 72


Correct answer : (1)
 2.  
The lines l and m are parallel. Find the values of x and y in the figure shown.

a.
x = 10 and y = 5
b.
x = 5 and y = 20
c.
x = 10 and y = 20
d.
x = 5 and y = 10


Solution:

If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
[Corresponding angles postulate.]

13y° = (20x + 3y
[Corresponding angles.]

10y = 20x y = 2x
[Simplify.]

13y° + (8x + y)° = 180°
[Adjacent angles.]

14y + (8x) = 180°
[Simplify.]

14(2x) + 8x = 180 36x = 180
[Substitute y = 2x and simplify.]

x = 180 / 36 x = 5
[Simplify.]

y = 2(5) = 10
[From step 3.]

So, the values of x and y are 5 and 10.


Correct answer : (4)
 3.  
If p and q are parallel and mA = 100, find the m1 and m2.

a.
m1 = 80 and m2 = 100
b.
m1 = 100 and m2 = 80
c.
m1 = 200 and m2 = 50
d.
m1 = 260 and m2 = 100


Solution:

If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
[Corresponding angles postulate.]

1 = 100°
[Corresponding angles.]

1 + 2 = 180°
[Adjacent angles.]

100° + 2 = 180°

2 = 180°- 100°

2 = 80°

Hence m1 = 100 and m2 = 80


Correct answer : (2)
 4.  
Find the values of 1 and 2 in the figure.

a.
1 = 60° and 2 = 100°
b.
1 = 60° and 2 = 80°
c.
1 = 100° and 2 = 60°
d.
1 = 80° and 2 = 100°


Solution:

MNO + 60° = 180°
[Adjacent angles.]

MNO = 180° - 60° = 120°
[Simplify.]

If two parallel lines are cut by a transversal, then corresponding angles are congruent.
[Alternate interior angle theorem.]

2 = 60°
[MN and OP are parallel lines cut by a transversal NO.]

If two parallel lines are cut by a transversal, then the pairs of Same-side interior angles are supplementary.
[Same-side interior angles theorem.]

1 + 80° = 180°
[MN and OP are parallel lines cut by a transversal MP.]

1 = 180° - 80° = 100°
[Simplify.]

Hence 1 = 60° and 2 = 100°


Correct answer : (1)
 5.  
Find the values of m1 and m2 in the figure.

a.
m1 = 120 and m2 = 60
b.
m1 = 80 and m2 = 100
c.
m1 = 80 and m2 = 80
d.
m1 = 100 and m2 = 100


Solution:

If two parallel lines are cut by a transversal, then the pairs of Same-side interior angles are supplementary.
[Same-side interior angles theorem.]

1 + 100° = 180°
[AB and DC are parallel lines cut by a transversal AD.]

1 = 180° - 100° = 80°
[Simplify.]

m1 + m2 = 180
[Alternate interior angles.]

80 + m2 = 180
[From step 3.]

m2 = 180 - 80 = 100
[Simplify.]

So, m1 = 80 and m2 = 100


Correct answer : (2)
 6.  
The lines p and q are parallel. Find the values of x and y.


a.
x = 16 and y = 20
b.
x = 32 and y = 20
c.
x = 16 and y = 80
d.
x = 20 and y = 60


Solution:

4x° + (6x + y)° = 180°
[Adjacent angles.]

10x + y = 180 ---------- (1)
[Simplify.]

If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
[Corresponding angles postulate.]

(6x + y)° = (x + 5y
[Corresponding angles.]

5x - 4y = 0 ---------- (2)
[Simplify.]

Solving equations (1) and (2), 45x = 720
[From steps (2) and (5).]

x = 16

5(16) - 4y = 0
[Substitute the value of x in equation (2).]

y = 20

So, the values of x and y are 16 and 20.


Correct answer : (1)
 7.  
The lines a and b are parallel. Find the mM and mP.


a.
mM = 135 and mN = 1150
b.
mM = 120 and mN = 100
c.
mM = 100 and mN = 80
d.
mM = 130 and mN = 110


Solution:

If two parallel lines are cut by a transversal, then the pairs of Same-side interior angles are supplementary.
[Same-side interior angles theorem.]

a° + (a - 20)° = 180°
[Same-side interior angles.]

2a = 200 a = 100
[Simplify.]

M = a° = 100°
[From step 3.]

P = (a - 20)° = (100 - 20)° = 80°
[From the figure.]

So, mM = 100 and mP = 80.


Correct answer : (3)
 8.  
Find the measures of A and B if the lines AB and CD are parallel to each other.

a.
m A = 115 and m B = 65
b.
m A = 55 and m B = 35
c.
m A = 70 and m B = 35
d.
m A = 15 and m B = 165


Solution:

If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
[Alternate interior angle theorem.]

B = D = x°
[Alternate interior angles.]

COD = AOB =90°
[Vertically opposite angles.]

(2x - 15)° + 90° + x = 180
[Sum of the angles in a triangle is 180°.]

3x = 105 x = 35
[Simplify.]

A = (2x - 15)
[From the figure.]

2(35) - 15 = 55°

mB = x = 35

So, the mA = 55 and mB = 35


Correct answer : (2)
 9.  
Find the value of x.


a.
60
b.
50
c.
45
d.
40


Solution:

If two parallel lines are cut by a transversal, then corresponding angles are congruent.
[Corresponding angles postulate.]

QPR = SRT = 40°
[Corresponding angles.]

40° + 90° + x° = 180°
[Sum of the angles in a triangle is 180°.]

x° = 50°
[Simplify.]

So, the value of x is 50.


Correct answer : (2)
 10.  
If m2 = m7 and line l is parallel to line m, then which of the following is true?
1. Line n is perpendicular to lines l and m.
2. All the angles 1 to 8 are equal.


a.
1 only
b.
1 or 2
c.
1 and 2
d.
2 only


Solution:

2 = 6
[l || m, corresponding angles are equal.]

m6 + m7 = 180
[Adjacent angles.]

m2 = m7
[As per the question.]

m6 = m7 = 90
[Steps 1 and 2.]

Line n is perpendicular to line m.
[Step 4.]

m5 = m8 = 90 = m6 = m7
[Step 5.]

Line n is perpendicular to line l.
[Line l and m are parallel.]

m1 = m2 = 90 = m3 = m4
[Step 7.]

So, both the statements are correct.


Correct answer : (3)

*AP and SAT are registered trademarks of the College Board.