# PARALLEL LINES CUT BY A 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.   Corresponding Angles :

∠CGE and ∠AHG, ∠DGE and ∠BHG, ∠CGH and ∠AHF, ∠DGH and ∠BHF ; congruent.

Alternate Interior Angles :

∠CGH and ∠BHG, ∠DGH and ∠AHG ; congruent.

Alternate Exterior Angles :

∠CGE and ∠BHF, ∠DGE and ∠AHF ; congruent.

Same-Side Interior Angles :

∠CGH and ∠AHG, ∠DGH and ∠BHG ; supplementary. 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°

Plug 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

So,

x  =  30° 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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