Question

solving for unknown values
use parallelogram abcd. what are the values of x and y?

Explanation:

Step1: Use the property of parallelogram (opposite sides are equal)

For side \(AD\) and \(BC\): \(3x - 9=42\)
For side \(AB\) and \(DC\): \(4y - 3 = 37\)

Step2: Solve for \(x\)

$$\begin{align*} 3x-9&=42\\ 3x&=42 + 9\\ 3x&=51\\ x&=\frac{51}{3}\\ x& = 17 \end{align*}$$

Step3: Solve for \(y\)

$$\begin{align*} 4y-3&=37\\ 4y&=37+ 3\\ 4y&=40\\ y&=\frac{40}{4}\\ y&=10 \end{align*}$$

Answer:

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