Let's analyze the problem.

The question involves parallelogram $ABCD$, where two angles are labeled as:

• $\angle A = (x + 40)^\circ$
• $\angle D = (x - 40)^\circ$.

Step 1: Properties of a parallelogram

In any parallelogram:

1. Opposite angles are equal.
2. Adjacent angles are supplementary (i.e., they add up to $180^\circ$).

Here, $\angle A$ and $\angle D$ are adjacent angles, so: $\angle A + \angle D = 180^\circ$

Step 2: Substitute the given angles

We are given: $\angle A = (x + 40)^\circ \quad \text{and} \quad \angle D = (x - 40)^\circ.$

Substitute these into the equation for supplementary angles: $(x + 40) + (x - 40) = 180$

Step 3: Simplify the equation

Combine like terms: $x + 40 + x - 40 = 180$ $2x = 180$

Step 4: Solve for $x$

Divide both sides by 2: $x = 90$

Final Answer:

The value of $x$ is 90.

Let me know if you'd like a more detailed explanation or if you have other questions. Here are some related questions to explore further:

1. What are the properties of the diagonals in a parallelogram?
2. How can you prove that opposite angles in a parallelogram are equal?
3. If two adjacent angles in a quadrilateral add up to $180^\circ$, is the shape always a parallelogram?
4. What are the formulas to find the area of a parallelogram?
5. How can we determine the missing angles in a parallelogram if only one angle is given?

Tip: In a parallelogram, the sum of adjacent angles is always $180^\circ$. Use this property to find unknown angles.