PARALLEL LINES AND TRANSVERSAL WORKSHEET

Problem 1 :

Identify the pairs of angles in the diagram. Then make a conjecture about their angle measures.

Problem 2 :

In the figure given below,  let the lines l1 and l2 be parallel and m is transversal. If F = 65°, find the measure of each of the remaining angles.

Problem 3 :

In the figure given below,  let the lines l1 and l2 be parallel and t is transversal. Find the value of 'x'.

Problem 4 :

In the figure given below,  let the lines l1 and l2 be parallel and t is transversal. Find the value of 'x'.

1. Answer :


Vertically opposite angles are equal.

1 = 3

2 = 4

5 = 7

6 = 8


Corresponding angles are equal.

1 = 5

2 = 6

3 = 7

4 = 8

Alternate interior  angles  are equal.

3 = 5

4 = 6

Alternate exterior angles  are equal.

1 = 7

2 = 8

Consecutive interior angles are supplementary.

3 + 6 = 180°

4 + 5 = 180°

Same side exterior angles are supplementary.

1 + 8 = 180°

2 + 7 = 180°

2. Answer :

From the given figure,

F and H are vertically opposite angles and they are equal.

Then, H = F ----> H = 65°.

H and D are corresponding angles and they are equal. 

Then, D = H ----> D = 65.°

D and B are vertically opposite angles and they are equal.

Then, B = D ----> B = 65°.

F and E are together form a straight angle.

Then, we have

F + E = 180°

Substitute F = 65°.

F + E = 180°

65° + E = 180°

E = 115°

E and G are vertically opposite angles and they are equal.

Then, G = E ----> G = 115°.

G and C are corresponding angles and they are equal.

Then, C = G ----> C = 115°.

C and A are vertically opposite angles and they are equal.

Then, A = C ----> A = 115°.

Therefore,

A = C = E = G = 115°

B = D = F = H = 65°

3. Answer :

From the given figure,

(2x + 20)° and (3x - 10)° are corresponding angles.

So, they are equal.

Then, we have

2x + 20 = 3x - 10

30 = x

4. Answer :

From the given figure,

(3x + 20)° and 2x° are consecutive interior angles.

So, they are supplementary.

Then, we have

3x + 20 + 2x = 180

5x + 20 = 180

5x = 160

x = 32

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