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 |

The pairs of corresponding angles in the figure shown are

So, from the given options,

Correct answer : (2)

2.

a. | 80 ^{o} | ||

b. | 100 ^{o} | ||

c. | 90 ^{o} | ||

d. | None of the above |

[From the figure.]

[Vertical angles are congruent.]

[From the figure.]

[Sum of supplementary angles is 180

[Substitute

[From the figure.]

[Alternate interior angles are congruent.]

[From the figure.]

[Vertical angles are congruent.]

So,

Correct answer : (3)

3.

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

a. | Ã |

In the figure,

In the choices, except for

So,

Correct answer : (-1)

4.

a. | 90° | ||

b. | 60° | ||

c. | 50° | ||

d. | 40° |

3

[Divide by 3 on each side.]

So,

Correct answer : (4)

5.

a. | 60 ^{o} | ||

b. | 30 ^{o} | ||

c. | 50 ^{o} | ||

d. | 65 ^{o} |

[Since the sum of the angles in a triangle = 180

130

[Substitute m

m

[Subtract 130

m

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

Since, corresponding angles are congruent, m

So, m

Correct answer : (3)

6.

a. | 50 ^{o} | ||

b. | 60 ^{o} | ||

c. | 90 ^{o} | ||

d. | 40 ^{o} |

3

[Divide by 3 on each side.]

So,

Correct answer : (4)

7.

Find the measure of $\angle $$q$ in the figure.

a. | 70 ^{o} | ||

b. | 110 ^{o} | ||

c. | 90 ^{o} | ||

d. | 50 ^{o} |

[Since vertical angles are congruent.]

Let

So,

So,

110

[Substitute the value of

So,

[Subtract 110

Correct answer : (1)

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 |

[Since, they are corresponding angles.]

5

[Add 70 to each side.]

[Subtract 3

So,

105° +

[Substitute the value of

[Subtract 105° from each side and simplify.]

So,

Correct answer : (1)

9.

a. | 60 ^{o} | ||

b. | 40 ^{o} | ||

c. | 50 ^{o} | ||

d. | 90 ^{o} |

3

[Divide by 3 on each side.]

So,

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° |

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,

From the diagram,

Sum of the supplementary angles = 180°

Sum of the supplementary angles = 180°

70° +

[Substitute.]

70° +

[Substitute.]

[Simplify.]

[Simplify.]

Correct answer : (3)