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Parallel Lines Worksheets

Parallel Lines Worksheets
  • Page 1
 1.  
Identify the corresponding angles in the figure.


a.
1 and 7, 2 and 8
b.
1 and 6, 2 and 5
c.
3 and 6, 4 and 5
d.
1 and 3, 2 and 4


Solution:

One interior and one exterior angle that lie on the same side of a transversal, and which do not form a pair of adjacent angles, are called corresponding angles.

The pairs of corresponding angles in the figure shown are 1 and 6, 2 and 5, 3 and 7, 4 and 8.

So, from the given options, 1 and 6, 2 and 5 are the corresponding angles.


Correct answer : (2)
 2.  
AB and CD are two parallel lines and x = 90o. Find the measures of 1, 4, and 6.


a.
80o
b.
100o
c.
90o
d.
None of the above


Solution:

x and 2 are vertical angles.
[From the figure.]

x = 2 = 90o
[Vertical angles are congruent.]

1 and 2 are supplementary angles.
[From the figure.]

1 + 2 = 180o
[Sum of supplementary angles is 180o.]

1 = 180o - 2 = 90o
[Substitute 2 = 90o.]

2 and 4 are alternate interior angles.
[From the figure.]

4 = 2 = 90o
[Alternate interior angles are congruent.]

4 and 6 are vertical angles.
[From the figure.]

6 = 4 = 90o
[Vertical angles are congruent.]

So, 1 = 4 = 6 = 90o


Correct answer : (3)
 3.  
The lines AB and CD are parallel. From the options, find the pairs of angles that are not congruent.
a.
Ð


Solution:

When a transversal intersects two parallel lines, the corresponding angles are congruent.

In the figure, 1 and 8, 2 and 5, 3 and 6, 4 and 7 are the corresponding angles.

In the choices, except for 4 and 3, all the others are corresponding angles.

So, 4 and 3 are not congruent.


Correct answer : (-1)
 4.  
AB and CD are two parallel lines with EF as the transversal. Find the value of x.

a.
90°
b.
60°
c.
50°
d.
40°


Solution:

If a transversal intersects two parallel lines, the alternate interior angles are congruent.

3x = 120°

x = 120 / 3
[Divide by 3 on each side.]

So, x = 40°.


Correct answer : (4)
 5.  
PQ is a line parallel to the base BC of ΔABC. What is the mAQP, if mA + mB = 130o?

a.
60o
b.
30o
c.
50o
d.
65o


Solution:

In ΔABC, mA + mB + mC = 180o
[Since the sum of the angles in a triangle = 180o.]

130o + mC = 180o
[Substitute mA + mB = 1300.]

mC = 180o - 130o
[Subtract 130o from each side.]

mC = 50o

In the ΔABC, PQ is parallel to BC and AC is the transversal.

AQP and C are corresponding angles.

Since, corresponding angles are congruent, mAQP = mC = 50o.

So, mAQP is 50o.


Correct answer : (3)
 6.  
AB, CD are two parallel lines and EF is the transversal. Find the value of x.


a.
50o
b.
60o
c.
90o
d.
40o


Solution:

If a transversal intersects two parallel lines, the alternate interior angles are congruent.

3x = 120o

x = 120 / 3
[Divide by 3 on each side.]

So, x = 40o.


Correct answer : (4)
 7.  
Find the measure of q in the figure.


a.
70o
b.
110o
c.
90o
d.
50o


Solution:

Let p be the vertical angle of 110o. p = 110o.
[Since vertical angles are congruent.]


Let r be the corresponding angle of 'p'.
So, mr = mp = 110o.

r and q are supplementary.
So, mr + mq = 180o.

110o + mq = 180o
[Substitute the value of r.]

So, mq = 70o.
[Subtract 110o from each side.]


Correct answer : (1)
 8.  
Find the measures of a and b.


a.
ma = m b = 75°
b.
ma = mb = 65°
c.
ma = 65° and mb = 75°
d.
None of the above


Solution:

(5x - 70)° = 3x°
[Since, they are corresponding angles.]

5x = 3x + 70
[Add 70 to each side.]

x = 35°
[Subtract 3x from each side and simplify.]

x = 35° then 3x = 3(35°) = 105°

3x and b are supplementary angles.

So, 3x + mb = 180°

105° + mb = 180°
[Substitute the value of 3x.]

mb = 75°
[Subtract 105° from each side and simplify.]

a and b are corresponding angles.
So, ma = 75°

ma = mb = 75°.


Correct answer : (1)
 9.  
AB, CD are two parallel lines and EF is the transversal. Find the value of x.

a.
60o
b.
40o
c.
50o
d.
90o


Solution:

If a transversal intersects two parallel lines, the alternate interior angles are congruent.

3x = 120o

x = 120 / 3
[Divide by 3 on each side.]

So, x = 40o.


Correct answer : (2)
 10.  
The road displayed in the diagram divides a farm into two parts. The opposite edges of the field are parallel, and the road is transversal. If m∠e is 70°, find m∠b.

a.
100°
b.
210°
c.
110°
d.
200°


Solution:


From the real-time picture, we can draw the required model transversal as follows.


From the real-time picture, we can draw the required model transversal as follows.

From the diagram, m∠e and m∠a are corresponding angles. And the corresponding angles are congruent.

From the diagram, m∠e and m∠a are corresponding angles. And the corresponding angles are congruent.

m∠e = m∠a = 70°

m∠e = m∠a = 70°

m∠a and m∠b are adjacent supplementary angles.

m∠a and m∠b are adjacent supplementary angles.

Sum of the supplementary angles = 180°

Sum of the supplementary angles = 180°

m∠a + m∠b = 180°

m∠a + m∠b = 180°

70° + m∠b = 180°
[Substitute.]

70° + m∠b = 180°
[Substitute.]

m∠b = 110°
[Simplify.]

m∠b = 110°
[Simplify.]


Correct answer : (3)

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