Alternate angles :
When two parallel lines are cut by a third line, then angles in alternate positions are equal in size.
Find the value of unknown of the following :
Problem 1 :
Solution :
Considering the angles marked in the picture given above are in alternate position, they are alternate opposite angles.
x + 10 = 2x - 25
Subtracting 2x on both sides.
x - 2x + 10 = -25
Subtracting 10 on both sides.
-x = -25 - 10
-x = -35
x = 35
Problem 2 :
Solution :
x = 61° (Alternate interior angles)
Problem 3 :
Solution :
21x + 6 and 22x + 2 are alternate interior angles.
21x + 6 = 22x + 2
Subtracting 22x on both sides.
21x - 22x + 6 = 2
Subtracting 6 on both sides.
-x = 2 - 6
x = 4
Problem 4 :
Solution :
12x + 8 and 13x + 2 are alternate interior angles.
12x + 8 = 13x + 2
Subtracting 13x on both sides.
12x - 13x + 8 = 2
Subtracting 8 on both sides.
-x = 2 - 8
x = 6
Problem 5 :
Solution :
28x + 3 and 29x - 1 are alternate interior angles.
28x + 3 = 29x - 1
Subtracting 29x on both sides.
28x - 29x + 3 = -1
Subtracting 3 on both sides.
-x = -1 - 3
x = 4
Problem 6 :
Solution :
19x - 3 and 130 are alternate interior angles.
19x - 3 = 130
Add 3 on both sides.
19x = 130 + 3
19x = 133
Dividing by 19 on both sides.
x = 133/19
x = 7
Problem 7 :
Solution :
x + 146 and 135 are alternate interior angles.
x + 146 = 135
x = 135 - 146
x = -11
Problem 8 :
Solution :
14x - 2 and 110 are alternate exterior angles.
14x - 2 = 110
Adding 2 on both sides.
14x = 110 + 2
14x = 112
Dividing by 14 on both sides.
x = 112/14
x = 8
Problem 9 :
Solution :
11x - 7 and 125 are alternate exterior angles.
11x - 7 = 125
Adding 7 on both sides.
11x = 125 + 7
11x = 132
Dividing by 11 on both sides.
x = 132/11
x = 12
Problem 10 :
Solution :
14x + 4 and 13x + 13 are alternate exterior angles.
14x + 4 = 13x + 13
Subtracting 13x on both sides.
14x - 13x + 4 = 13
x + 4 = 13
Subtracting 4 on both sides.
x = 13 - 4
x = 9
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM