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.
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
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
May 02, 24 02:57 AM
Apr 30, 24 09:01 PM
Apr 30, 24 08:50 PM