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:

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