Parallel lines cut by a transversal worksheet answers

A line that intersects two or more other lines is called a transversal. When a transversal intersects two parallel lines, it creates eight angles that include corresponding angles, alternate interior angles, alternate exterior angles, and same-side interior angles. In this eighth-grade geometry worksheet, students will practice identifying these different types of angle pairs using given diagrams. Students will then use those angle relationships to find missing angle measures on two other diagrams and explain how they found the missing angle measures. For more practice with parallel lines cut by a transversal, complete the Transversals of Parallel Lines 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.

Answers

1. Answer :

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.

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°

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°

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

So,

x  =  30°

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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