#### Solved Examples and Worksheet for Parallel Lines and Transversals

Q1Find the value of x, if y = 35° and b = 70°. A. 75°
B. 205°
C. 145°
D. 110°

Step: 1
a + 35° = 70°
[Alternate Interior Angles Theorem.]
Step: 2
a = 35°
[Simplify.]
Step: 3
a + x = 180°
[Same-Side Interior Angles Theorem.]
Step: 4
35° + x = 180°
[Substitute.]
Step: 5
x = 145°
[Simplify.]
Q2mECB = 140°, find mABC. A. 40°
B. 140°
C. 50°
D. 320°

Step: 1
mECD = 180°
[ECD is a straight angle.]
Step: 2
mECB + mBCD = 180°
Step: 3
140° + mBCD = 180°
[Substitute.]
Step: 4
mBCD = 40°
[Simplify.]
Step: 5
mABC = mBCD
[Alternate Interior Angles Theorem.]
Step: 6
mABC = 40°
[Substitute.]
Q3In the following figure, two parallel lines are cut by a transversal. Find x. A. 13
B. 52
C. 106
D. 117
E. 128

Step: 1
The two labeled angles are supplementary angles and hence their sum is equal to 180o.
Step: 2
4x + 9x + 11 = 180
Step: 3
13x + 11 = 180
Step: 4
13x = 169 x = 13
Q4If p and q are parallel and mA = 125, find the m1 and m2. A. m1 = 250 and m2 = 62
B. m1 = 55 and m2 = 125
C. m1 = 125 and m2 = 55
D. m1 = 235 and m2 = 125

Step: 1
If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
[Corresponding angles postulate.]
Step: 2
1 = 125°
[Corresponding angles.]
Step: 3
1 + 2 = 180°
[Linear Pair.]
Step: 4
125° + 2 = 180°
Step: 5
2 = 180°- 125°
Step: 6
2 = 55°
Step: 7
Hence m1 = 125 and m2 = 55
Correct Answer is :   m1 = 125 and m2 = 55
Q5Find the value of x. A. 140
B. 120
C. 110
D. 60
E. 100

Step: 1
From the figure, x° = 2y° 12x° = y°
[Alternate angles.]
Step: 2
From the figure, x° + y° = 180°
[Supplementary angles.]
Step: 3
x° + y° = 180° x° + 12x° = 180°
[From step 1 and step 2.]
Step: 4
x° = 120°.
[Solve for x.]
Q6Two parallel lines L1 and L2 are cut by a transversal T. Use the figure to find how are 4 and 5 related. A. complementary.
B. congruent.
C. supplementary.
D. none of the above

Step: 1
4 + 5 = 180o
[Same-Side Interior Angles Theorem.]
Step: 2
4 and 5 are Supplementary.
[Step 1.]
Q7Find the measures of 1 and 2, if mA equals 135. A. m1 = 45 and m2 = 135
B. m1 = 270 and m2 = 67
C. m1 = 225 and m2 = 135
D. m1 = 135 and m2 = 45

Step: 1
If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
[Corresponding angles postulate.]
Step: 2
1 = 135°
[Corresponding angles.]
Step: 3
1 + 2 = 180°
Step: 4
135° + 2 = 180°
Step: 5
2 = 180°- 135°
Step: 6
2 = 45°
Step: 7
Hence m1 = 135 and m2 = 45
Correct Answer is :   m1 = 135 and m2 = 45
Q8mECB = 130, find mABC. A. 310
B. 130
C. 50
D. 40

Step: 1
mECD = 180
[ECD is a straight angle.]
Step: 2
mECB + mBCD = 180
Step: 3
130 + mBCD = 180
[Substitute.]
Step: 4
mBCD = 50
[Simplify.]
Step: 5
mABC = mBCD
[Alternate Interior Angles Theorem.]
Step: 6
mABC = 50
[Substitute.]
Q9Find the value of x. A. 90°
B. 30°
C. 60°
D. 45°

Step: 1
In a parallelogram adjacent angles are supplementary .
Step: 2
x + 3x = 180°
Step: 3
4x = 180° x = 45°
[Simplify.]
Q10mECB = 160, find mABC. A. 340
B. 160
C. 20
D. 115

Step: 1
mECD = 180
[ECD is a straight angle.]
Step: 2
mECB + mBCD = 180
Step: 3
160 + mBCD = 180
[Substitute.]
Step: 4
mBCD = 20
[Simplify.]
Step: 5
mABC = mBCD
[Alternate Interior Angles Theorem.]
Step: 6
mABC = 20
[Substitute.]
Q11Find the m1 and m2 in the figure shown. A. m∠1 = 60 and m∠2 = 120
B. m∠1 = 100 and m∠2 = 60
C. m∠1 = 120 and m∠2 = 60
D. m∠1 = 120 and m∠2 = 80

Step: 1
If two parallel lines are cut by a transversal, then the pairs of Same-side interior angles are supplementary.
[AB¯ and DC¯ are parallel lines cut by a transversal AD¯.]
Step: 2
∠1 + 120° = 180°
[Same - side interior angles theorm.]
Step: 3
∠1 = 180° - 120° = 60°
[Simplify.]
Step: 4
m∠1 + m∠2 = 180
[Same - side interior angles theorm.]
Step: 5
60 + m∠2 = 180
[From step 3.]
Step: 6
m∠2 = 180 - 60 = 120
[Simplify.]
Step: 7
So, m∠1 = 60 and m∠2 = 120
Correct Answer is :   m∠1 = 60 and m∠2 = 120
Q12The lines j and k are parallel. Find the values of x and y in the figure shown. [a = 10, b = 2.] A. x = 15 and y = 17
B. x = 15 and y = 150
C. x = 15 and y = 30
D. x = 7 and y = 14

Step: 1
10x° + 2x° = 180°
Step: 2
12x° = 180°
Step: 3
x° = 180°12 = 15°
Step: 4
If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
[Corresponding angles postulate .]
Step: 5
y = (2x)
[From step 4.]
Step: 6
y = 2(15) = 30
Step: 7
So, x = 15 and y = 30
Correct Answer is :   x = 15 and y = 30
Q13The lines l and m are parallel. Find the values of x and y in the figure shown. A. x = 6 and y = 18
B. x = 12 and y = 4
C. x = 4 and y = 8
D. x = 4 and y = 12

Step: 1
If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
[Corresponding angles postulate.]
Step: 2
12y° = (21x + 5y
[Corresponding angles.]
Step: 3
7y = 21x y = 3x
[Simplify.]
Step: 4
12y° + (6x + y)° = 180°
Step: 5
13y + (6x) = 180°
[Simplify.]
Step: 6
13(3x) + 6x = 180 45x = 180
[Substitute y = 3x and simplify.]
Step: 7
x = 18045 x = 4
[Simplify.]
Step: 8
y = 3(4) = 12
[From step 3.]
Step: 9
So, the values of x and y are 4 and 12.
Correct Answer is :   x = 4 and y = 12
Q14The lines p and q are parallel. Find the values of x. A. x = 40
B. x = 60
C. x = 50
D. x = 30

Step: 1
From the data, one of the large angles is (3x + y)°.
Step: 2
From the data, two of the small angles are 40° and (3x - y)°.
Step: 3
If a transversal intersects two or more parallel lines, all small angles are equal.
Therefore, 3x - y = 40 ---- (1)
Step: 4
If a transversal intersects two or more parallel lines, then sum of small angle and large angle equals straight angle.
Therefore, 3x + y + 40 = 180
3x + y = 140 ---- (2)
Step: 5
Now, add equation (1) and equation (2) and solve for x.
6x = 180
x = 30
Correct Answer is :   x = 30
Q15From the given figure If ECB = 150, then ABC = _________ . A. 30
B. 150
C. 330
D. 105

Step: 1
mECD = 180
[ECD is a straight angle.]
Step: 2
mECB + mBCD = 180