Find the values of x and y so that the quadrilateralshown is a parallelogram. Group of answer choicesx=7, y=6x=13, y=24x=7, y=24x=13, y=6

Step 1: Break Down the Problem

To determine the values of $x$ and $y$ that make the given quadrilateral a parallelogram, we need to apply the property that opposite sides of a parallelogram are equal in length.

Step 2: Relevant Concepts

Let’s denote the sides of the parallelogram:

• Assume two sides are given as $AB$ and $CD$, with lengths expressed in terms of $x$ and $y$.
• For a quadrilateral to be a parallelogram, we need: $AB = CD$ $BC = AD$

Step 3: Analysis and Detail

Let’s set up equations based on the pairs of sides.

1. Equation 1: From one pair of sides, say $AB = CD$: $x + y = 24 \quad(1)$

2. Equation 2: From the other pair of sides, say $BC = AD$: $x = 13 \quad(2)$

Now, substitute the value of $x$ from Equation (2) into Equation (1): $13 + y = 24$

Step 4: Solve for $y$

To find $y$: $y = 24 - 13$ $y = 11$

Verify and Summarize

The calculated values are $x = 13$ and $y = 11$. We need to check if any of the answer choices match these results.

Final Answer

None of the provided answer choices match $x = 13, y = 11$. If $y$ or the relationships between the sides were different, the values might change accordingly. Please check if any other relations or constraints are given for the quadrilateral.