﻿ Parallel Lines Worksheets | Problems & Solutions

# Parallel Lines Worksheets

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

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

2.
AB and CD are two parallel lines and $\angle$x = 90o. Find the measures of $\angle$1, $\angle$4, and $\angle$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

3.
The lines AB and CD are parallel. From the options, find the pairs of angles that are not congruent.
 a. Ã

#### 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.

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°.

5.
PQ is a line parallel to the base BC of ΔABC. What is the m$\angle$AQP, if m$\angle$A + m$\angle$B = 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.

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.

7.
Find the measure of $\angle$$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.]

8.
Find the measures of $\angle$$a$ and $\angle$$b$.

 a. $m$$\angle$$a$ = $m$ $\angle$$b$ = 75° b. $m$$\angle$$a$ = $m$$\angle$$b$ = 65° c. $m$$\angle$$a$ = 65° and $m$$\angle$$b$ = 75° d. None of the above

#### Solution:

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

5x = 3x + 70

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°.

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.

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.]