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 |

[Adjacent angles.]

5

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

[Corresponding angles postulate .]

[From step 4.]

So,

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 |

[Corresponding angles postulate.]

13

[Corresponding angles.]

10

[Simplify.]

13

[Adjacent angles.]

14

[Simplify.]

14(2

[Substitute

[Simplify.]

[From step 3.]

So, the values of

Correct answer : (4)

3.

If $p$ and $q$ are parallel and $m$$\angle $$A$ = 100, find the $m$$\angle $1 and $m$$\angle $2.

a. | $m$$\angle $1 = 80 and $m$$\angle $2 = 100 | ||

b. | $m$$\angle $1 = 100 and $m$$\angle $2 = 80 | ||

c. | $m$$\angle $1 = 200 and $m$$\angle $2 = 50 | ||

d. | $m$$\angle $1 = 260 and $m$$\angle $2 = 100 |

[Corresponding angles postulate.]

[Corresponding angles.]

[Adjacent angles.]

100° +

Hence

Correct answer : (2)

4.

Find the values of $\angle $1 and $\angle $2 in the figure.

a. | $\angle $1 = 60° and $\angle $2 = 100° | ||

b. | $\angle $1 = 60° and $\angle $2 = 80° | ||

c. | $\angle $1 = 100° and $\angle $2 = 60° | ||

d. | $\angle $1 = 80° and $\angle $2 = 100° |

[Adjacent angles.]

[Simplify.]

If two parallel lines are cut by a transversal, then corresponding angles are congruent.

[Alternate interior angle theorem.]

[

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

[Same-side interior angles theorem.]

[

[Simplify.]

Hence

Correct answer : (1)

5.

Find the values of $m$$\angle $1 and $m$$\angle $2 in the figure.

a. | $m$$\angle $1 = 120 and $m$$\angle $2 = 60 | ||

b. | $m$$\angle $1 = 80 and $m$$\angle $2 = 100 | ||

c. | $m$$\angle $1 = 80 and $m$$\angle $2 = 80 | ||

d. | $m$$\angle $1 = 100 and $m$$\angle $2 = 100 |

[Same-side interior angles theorem.]

[

[Simplify.]

[Alternate interior angles.]

80 +

[From step 3.]

[Simplify.]

So,

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 |

[Adjacent angles.]

10

[Simplify.]

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

[Corresponding angles postulate.]

(6

[Corresponding angles.]

5

[Simplify.]

Solving equations (1) and (2), 45

[From steps (2) and (5).]

5(16) - 4

[Substitute the value of

So, the values of

Correct answer : (1)

7.

The lines $a$ and $b$ are parallel. Find the $m$$\angle $M and $m$$\angle $P.

a. | $m$$\angle $M = 135 and $m$$\angle $N = 1150 | ||

b. | $m$$\angle $M = 120 and $m$$\angle $N = 100 | ||

c. | $m$$\angle $M = 100 and $m$$\angle $N = 80 | ||

d. | $m$$\angle $M = 130 and $m$$\angle $N = 110 |

[Same-side interior angles theorem.]

[Same-side interior angles.]

2

[Simplify.]

[From step 3.]

[From the figure.]

So,

Correct answer : (3)

8.

Find the measures of $\angle $A and $\angle $B if the lines AB and CD are parallel to each other.

a. | $m$ $\angle $A = 115 and $m$ $\angle $B = 65 | ||

b. | $m$ $\angle $A = 55 and $m$ $\angle $B = 35 | ||

c. | $m$ $\angle $A = 70 and $m$ $\angle $B = 35 | ||

d. | $m$ $\angle $A = 15 and $m$ $\angle $B = 165 |

[Alternate interior angle theorem.]

[Alternate interior angles.]

[Vertically opposite angles.]

(2

[Sum of the angles in a triangle is 180°.]

3

[Simplify.]

[From the figure.]

So, the

Correct answer : (2)

9.

Find the value of $x$.

a. | 60 | ||

b. | 50 | ||

c. | 45 | ||

d. | 40 |

[Corresponding angles postulate.]

[Corresponding angles.]

40° + 90° +

[Sum of the angles in a triangle is 180°.]

[Simplify.]

So, the value of

Correct answer : (2)

10.

If $m$$\angle $2 = $m$ $\angle $7 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.

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 |

[

[Adjacent angles.]

[As per the question.]

[Steps 1 and 2.]

Line

[Step 4.]

[Step 5.]

Line

[Line

[Step 7.]

So, both the statements are correct.

Correct answer : (3)