JUSTIFYING ANGLE RELATIONSHIPS WORKSHEET

Problem 1 :

A transversal cuts the two parallel lines and forms eight angles.  Describe the relationships between the angles in the diagram given below. 

Problem 2 :

In the figure given below, let the lines l1 and l2 be parallel and m is transversal. If F = 65°, using the angle relationships,  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. Using angle relationships, find the value of x.

Problem 4 :

In the figure given below, let the lines l1 and l2 be parallel and t is transversal. Using angle relationships, find the value of x.

Answers

Problem 1 :

A transversal cuts the two parallel lines and forms eight angles.  Describe the relationships between the angles in the diagram given below. 

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.

Problem 2 : 

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

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°

Problem 3 :

In the figure given below,  let the lines l1 and l2 be parallel and t is transversal. Using angle relationships, find the value of x.

Answer :

From the given figure, 

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

So, they are equal. 

Then, we have

(2x + 20)°  =  (3x - 10)°

2x + 20  =  3x - 10

30  =  x

Problem 4 : 

In the figure given below,  let the lines l1 and l2 be parallel and t is transversal. Using angle relationships, find the value of x.

Answer :

From the given figure, 

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

So, they are supplementary. 

Then, we have

(3x + 20)° + 2x°  =  180°

3x + 20 + 2x  =  180

5x + 20  =  180

5x  =  160

x  =  32

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