Problem Analysis:

The figure is a rhombus $ZYXW$. A rhombus has the following properties:

1. All sides are equal in length.
2. Opposite angles are equal.
3. Diagonals bisect each other at right angles (90°).
4. The diagonals divide the rhombus into four congruent right triangles.

The given information:

• $m\angle WXY = (8b + 4)^\circ$
• $m\angle YWX = (6b + 18)^\circ$

Since $ZYXW$ is a rhombus, the diagonals bisect the interior angles. Thus: $m\angle WXY + m\angle YWX = 90^\circ$

Step-by-Step Solution:

Using the relationship between the angles: $(8b + 4) + (6b + 18) = 90$ Simplify: $14b + 22 = 90$ Subtract 22 from both sides: $14b = 68$ Divide by 14: $b = \frac{68}{14} = \frac{34}{7} \approx 4.857$

Thus, $b = \frac{34}{7}$.

Would you like a detailed breakdown of the solution or further clarification?
Here are 5 related questions to deepen understanding:

1. What are the general properties of a rhombus, and how are they applied in angle calculations?
2. How do diagonals of a rhombus divide it into congruent triangles?
3. Why is the sum of two adjacent angles of a rhombus equal to 90°?
4. How would the solution change if the angle measurements were different?
5. Can this method of solving work for other quadrilaterals? Why or why not?

Tip:

Always verify the relationships between angles when solving geometric problems involving specific quadrilaterals like rhombuses, squares, or rectangles.