Question

use parallelogram abcd. what are the values of x and y? x = y = a b 4y - 3 3x - 9 42 d 37 c

Explanation:

Step1: Solve for x (opposite sides of parallelogram are equal)

In a parallelogram, opposite sides are equal. So, \( AD = BC \). Given \( AD = 3x - 9 \) and \( BC = 42 \).
\[
3x - 9 = 42
\]
Add 9 to both sides:
\[
3x = 42 + 9 = 51
\]
Divide both sides by 3:
\[
x = \frac{51}{3} = 17
\]

Step2: Solve for y (opposite sides of parallelogram are equal)

In a parallelogram, opposite sides are equal. So, \( AB = DC \). Given \( AB = 4y - 3 \) and \( DC = 37 \).
\[
4y - 3 = 37
\]
Add 3 to both sides:
\[
4y = 37 + 3 = 40
\]
Divide both sides by 4:
\[
y = \frac{40}{4} = 10
\]

Answer:

\( x = 17 \)
\( y = 10 \)