# 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'.

 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°

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°

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

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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