In the provided image, we are tasked with solving for $x$ in a parallelogram. The key property of a parallelogram is that opposite angles are equal.

Given:

• $\angle B = 74^\circ$
• $\angle C = 25x + 6$

Since $\angle B$ and $\angle C$ are consecutive angles of a parallelogram, the sum of consecutive angles in a parallelogram is always $180^\circ$.

Thus, we can set up the following equation:

$\angle B + \angle C = 180^\circ$

Substitute the given values:

$74^\circ + (25x + 6) = 180^\circ$

Now, let's solve for $x$:

$74 + 25x + 6 = 180$ $80 + 25x = 180$ $25x = 180 - 80$ $25x = 100$ $x = \frac{100}{25}$ $x = 4$

Final Answer:

$x = 4$

Would you like a more detailed explanation or have any further questions?

Here are 5 related questions to expand your understanding:

1. How do opposite angles in a parallelogram compare?
2. What is the sum of the interior angles of any quadrilateral?
3. How do we solve for unknowns in geometric figures using algebra?
4. Can the properties of a parallelogram be used to solve problems involving side lengths as well?
5. What other types of quadrilaterals share similar angle properties to a parallelogram?

Tip: Always check if angle relationships like complementary or supplementary angles apply when solving geometry problems!