On a coordinate plane, 2 lines are shown. Line A B has points (negative 4, negative 2) and (4, 4). Line C D has points (0, negat
ive 3) and (4, 0). Which statement best explains the relationship between lines AB and CD? They are parallel because their slopes are equal. They are parallel because their slopes are negative reciprocals. They are not parallel because their slopes are not equal. They are not parallel because their slopes are negative reciprocals.
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Answer:
Step-by-step explanation:
Given that lines l and m are parallel and there is a transversal cutting through these lines.
5). (9x + 2)° = 119° [by alternate interior angles]
9x = 117 ⇒ x = 13
6). (12x - 8)° + 104° = 180°
12x = 180 - 96
x = ⇒ x = 7
7). (5x + 7) = (8x - 71) [by alternate exterior angles]
8x - 5x = 71 + 7
3x = 78
x = 26
8). (4x - 7) = (7x - 61) [by corresponding angles]
7x - 4x = -7 + 61
3x = 54
x = 18
9). (9x + 25) = (13x - 19) [by corresponding angles]
13x - 9x = 25 + 19
4x = 44
x = 11
(13x - 19)° + (17y + 5)° = 180° [linear pairs of angles sum to supplementary]
(13×11) - 19 + 17y + 5 = 180
129 + 17y = 180
17y = 180 - 129
y = 3
10). (3x - 29) + (8y + 17) = 180 [linear pairs of angles sum to supplementary]
3x + 8y = 180 + 12
3x + 8y = 192 -----(1)
(8y + 17) = (6x - 7) [by alternate exterior angles]
6x - 8y = 24
3x - 4y = 12 -----(2)
From equation (1) subtract equation (2)
(3x + 8y) - (3x - 4y) = 192 - 12
12y = 180
y = 15
Plugging into equation (1),
3x + 8(15) = 192
3x + 120 = 192
x = 24
11). (3x + 49)° = (7x - 23)° [by corresponding angles]
7x - 3x = 49 + 23
4x = 72 ⇒ x = 18
(11y - 1)° = (3x)° [by corresponding angles]
11y = 3×18 + 1
11y = 55 ⇒ y = 5
12). (5x - 38)° = (3x - 4)° [by corresponding angles]
5x - 3x = 38 - 4
2x = 34
x = 17
(7y - 20)° + (5x - 38)° + 90° = 180°
[The angles within a triangle sum to 180°]
7y + 5x - 58 = 90
5x + 7y = 148
5×17 + 7y = 148
85 + 7y = 148
7y = 148 - 85
y =