# PARALLEL LINES CUT BY A TRANSVERSAL WORKSHEET

## About "Parallel lines cut by a transversal worksheet"

Parallel lines cut by a transversal worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on parallel lines and transversals.

## Parallel lines cut by a transversal worksheet - Problems

1.  Identify the pairs of angles in the diagram. Then make a conjecture about their angle measures. 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. 3.  In the figure given below,  let the lines l₁ and l₂ be parallel and t is transversal. Find the value of "x" 4.  In the figure given below,  let the lines l₁ and l₂ be parallel and t is transversal. Find the value of "x"  ## Parallel lines cut by a transversal worksheet - Solution

Problem 1 :

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

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.

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. Solution :

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°

Problem 3 :

In the figure given below,  let the lines l₁ and l₂ be parallel and t is transversal. Find the value of "x" Solution :

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

Hence, x  =  30°

Problem 4 :

In the figure given below,  let the lines l₁ and l₂ be parallel and t is transversal. Find the value of "x" Solution :

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°

Hence, x  =  32° After having gone through the stuff given above, we hope that the students would have understood "Parallel lines cut by a transversal worksheet".

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