To solve for $x$, let's analyze the given parallelogram $ABCD$.

Step 1: Understanding the Properties of a Parallelogram

• Opposite sides are equal: $AB = CD$ and $AD = BC$.
• Opposite angles are equal: $\angle A = \angle C$ and $\angle B = \angle D$.
• Consecutive angles are supplementary: $\angle A + \angle D = 180^\circ$ and $\angle B + \angle C = 180^\circ$.

Step 2: Setting Up the Equation

From the diagram, we have:

• $BC = 2x + 7$
• $AD = 10$

Since opposite sides of a parallelogram are equal: $2x + 7 = 10$

Step 3: Solving for $x$

$2x = 10 - 7$ $2x = 3$ $x = \frac{3}{2}$

Final Answer:

$x = 1.5$

Would you like a detailed explanation of another part of the problem?

Related Questions:

1. How do we find the value of $y$ in the problem?
2. What are the properties of a parallelogram that help solve for unknown values?
3. How do we confirm that $ABCD$ is a parallelogram?
4. What is the sum of the interior angles of a parallelogram?
5. How can we use the diagonal properties of a parallelogram to find missing angles?

Tip:

In a parallelogram, diagonals bisect each other, which can be useful when solving for unknown angles and side lengths.