Question

find the value of ( x ) and ( y ) in the parallelogram below.

answer attempt 1 out of 2

( x = square ) ( y = square )

Explanation:

Step1: Solve for \( x \)

In a parallelogram, opposite sides are equal. So, the side with length \( -10x + 10 \) is equal to the opposite side with length \( 90 \).

$$ -10x + 10 = 90 $$

Subtract \( 10 \) from both sides:

$$ -10x = 90 - 10 $$

$$ -10x = 80 $$

Divide both sides by \( -10 \):

$$ x = \frac{80}{-10} $$

$$ x = -8 $$

Step2: Solve for \( y \)

Also, in a parallelogram, the side with length \( -2y - 6 \) is equal to the opposite side with length \( 144 \).

$$ -2y - 6 = 144 $$

Add \( 6 \) to both sides:

$$ -2y = 144 + 6 $$

$$ -2y = 150 $$

Divide both sides by \( -2 \):

$$ y = \frac{150}{-2} $$

$$ y = -75 $$

Answer:

\( x = -8 \), \( y = -75 \)