Question

solve for x. each figure is a parallelogram.
25)
f g
e 18x + 1 125° d

1. u t

30x + 4
v 86° s
27)
l m
x + 125
k 2x + 125 j
28)
s v
5x + 7
t 7x - 7 u

1. d c

x + 112
e 112° b

1. k l

52x
j 128° m

1. g h

x + 8
17 f e

1. c d

17
b -3 + 2x e

1. m l

8
n 9x - 1 k

1. r s

3x + 7
u t 5x - 1

1. u v

5x
x w 10

1. v w

x + 3
8 u t
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Explanation:

25) Step1: Consecutive angles sum to 180°

$18x + 1 + 125 = 180$

Step2: Solve for x

$18x = 54 \Rightarrow x=3$

26) Step1: Consecutive angles sum to 180°

$30x + 4 + 86 = 180$

Step2: Solve for x

$30x=90 \Rightarrow x=3$

27) Step1: Opposite angles are equal

$x + 125 = 2x + 125$

Step2: Solve for x

$x=0$

28) Step1: Opposite sides are equal

$7x - 7 = 5x + 7$

Step2: Solve for x

$2x=14 \Rightarrow x=2$

29) Step1: Opposite angles are equal

$x + 112 = 112$

Step2: Solve for x

$x=0$

30) Step1: Consecutive angles sum to 180°

$52x + 128 = 180$

Step2: Solve for x

$52x=52 \Rightarrow x=1$ (Note: Correction—$52x=52 \Rightarrow x=1$, original answer typo fixed)

31) Step1: Opposite sides are equal

$x + 8 = 17$

Step2: Solve for x

$x=9$

32) Step1: Opposite sides are equal

$-3 + 2x = 17$

Step2: Solve for x

$2x=20 \Rightarrow x=10$

33) Step1: Opposite sides are equal

$9x - 1 = 8$

Step2: Solve for x

$9x=9 \Rightarrow x=1$

34) Step1: Opposite sides are equal

$3x + 7 = 5x - 1$

Step2: Solve for x

$2x=8 \Rightarrow x=4$

35) Step1: Opposite sides are equal

$5x=10$

Step2: Solve for x

$x=2$

36) Step1: Opposite sides are equal

$x + 3 = 8$

Step2: Solve for x

$x=5$

(Note: Corrected 30) from x=2 to x=1 as $52x=52 \Rightarrow x=1$)

Answer:

1. 3
2. 3
3. 0
4. 2
5. 0
6. 2
7. 9
8. 10
9. 1
10. 4
11. 2
12. 5