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Which equation can be used to solve for x in the parallelogram below?

a) 6x + 12 = 2x + 8
b) 2x + 8 = 7x - 8
c) 3x - 12 = 6x + 12
d) 7x - 8 = 2x + 8

User EdG
by
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1 Answer

7 votes

Final answer:

We cannot determine the correct equation without additional information about the parallelogram. Normally, equations for parallelograms equate opposite sides or angles based on their properties of congruency and supplementary angles.

Step-by-step explanation:

In a parallelogram, opposite angles are equal, and consecutive angles are supplementary. Let's denote the angles in the parallelogram:

- ( ∠ A ) and ( ∠ C ) are opposite angles.

- ( ∠ A ) and ( ∠ B ) are consecutive angles.

- ( ∠ B ) and ( ∠ D ) are opposite angles.

- ( ∠ C ) and ( ∠ D ) are consecutive angles.

Since opposite angles are equal, we can set up an equation involving \( \angle A \) and \( \angle C \):

6x + 12 = 3x - 12

Now, solve for (x):

6x + 12 = 3x - 12

Combine like terms:

3x = -24

Divide by 3:

x = -8

Now, let's check which equation represents this relationship:

A. ( 6x + 12 = 1x - 8 ) (Not equivalent)

B. ( (3x + 12) + (1x - 8) = 90 ) (Equivalent)

C. ( 1x - 8 = 2 + 8 ) (Not equivalent)

D. ( (1x - 8) + (6x + 12) = 180 ) (Equivalent)

So, the correct equation is:

B. ( (3x + 12) + (1x - 8) = 90 )

your complete question is: Which equation can be used to solve for x in the parallelogram below?

(6x+12)8 (2x+8)8

(3x-12)9

(7x-8)9

A

6x + 12 = 1x - 8

B

(3x + 12) + (1x - 8) = 90

C

1x - 8 = 2 + 8

D

(1x - 8) + (6x + 12) = 180

User Chengmin
by
8.2k points