Let me analyze the problem in the uploaded image.

The problem shows a parallelogram $ABCD$, and the goal is to find the measure of angle $A$, denoted as $m \angle A$. The two adjacent angles are given as:

• $\angle A = (6x + 20)^\circ$
• $\angle D = (4x + 10)^\circ$

Key Properties of a Parallelogram:

1. Adjacent angles of a parallelogram are supplementary, i.e., their sum equals $180^\circ$:
   $\angle A + \angle D = 180^\circ$

Steps to Solve:

1. Use the supplementary property: $(6x + 20) + (4x + 10) = 180$

2. Simplify the equation: $10x + 30 = 180$

3. Solve for $x$: $10x = 150 \quad \Rightarrow \quad x = 15$

4. Substitute $x = 15$ into $m \angle A = 6x + 20$: $m \angle A = 6(15) + 20 = 90 + 20 = 110^\circ$

Final Answer:

$m \angle A = 110^\circ$

Would you like further clarification or steps explained?

Here are 5 related questions to expand this topic:

1. How do you calculate the measure of the other angles in the parallelogram?
2. What are other properties of a parallelogram involving diagonals or opposite angles?
3. How would the solution change if this were a rhombus?
4. Can you derive a general formula for solving similar problems in parallelograms?
5. What are the key differences between a parallelogram and a trapezium?

Tip: Always remember that adjacent angles in a parallelogram are supplementary while opposite angles are equal.