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 l_{1} and l_{2} 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 l_{1} and l_{2} be parallel and t is transversal. Find the value of 'x'.
Problem 4 :
In the figure given below, let the lines l_{1} and l_{2} be parallel and t is transversal. Find the value of 'x'.
1. Answer :
Vertically opposite angles are equal. |
∠1 = ∠3 ∠2 = ∠4 ∠5 = ∠7 ∠6 = ∠8 |
Corresponding angles are equal. |
∠1 = ∠5 ∠2 = ∠6 ∠3 = ∠7 ∠4 = ∠8 |
Alternate interior angles are equal. |
∠3 = ∠5 ∠4 = ∠6 |
Alternate exterior angles are equal. |
∠1 = ∠7 ∠2 = ∠8 |
Consecutive interior angles are supplementary. |
∠3 + ∠6 = 180° ∠4 + ∠5 = 180° |
Same side exterior angles are supplementary. |
∠1 + ∠8 = 180° ∠2 + ∠7 = 180° |
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°
Substitute ∠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
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
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Aug 06, 22 11:56 PM
Aug 06, 22 11:31 PM
Aug 06, 22 09:01 AM