Let's break down the problems in the image step by step:

Problem 1:

You are given a geometric diagram where:

• $\angle ABD = 57^\circ$
• $\angle DBC = 3x - 4$
• The total measure of $\angle ABC = 128^\circ$.

To find the value of $x$, you need to use the fact that the sum of the angles $\angle ABD$ and $\angle DBC$ must equal $\angle ABC$.

Thus, the equation will be: $\angle ABD + \angle DBC = \angle ABC$ Substitute the known values: $57^\circ + (3x - 4) = 128^\circ$ Now, solve for $x$: $57^\circ + 3x - 4 = 128^\circ$ $3x + 53 = 128^\circ$ $3x = 128^\circ - 53$ $3x = 75$ $x = \frac{75}{3} = 25$

So, $x = 25$.

Problem 2:

This looks like a puzzle box where arithmetic operations are applied to numbers inside the boxes. There are two possible ways to interpret the layout, but one common interpretation of this type of puzzle is that the operations link boxes either horizontally or vertically.

Without more context or clear rules, here's one approach:

• The top-left corner has "3+" which may mean adding 3.
• The top-right corner has "6x," which could indicate multiplying by 6.
• The bottom-left corner has "2-" which suggests subtracting 2.
• The bottom-right corner has "2÷," which implies division by 2.

If you're asked to perform these operations with linked numbers or if they relate to the given values in adjacent boxes, please clarify how the numbers are related for further analysis.

Would you like more details or clarification on either part of the solution? Here are some follow-up questions to help expand understanding:

1. What is the sum of angles in a triangle and how does it relate to the diagram?
2. Can you derive the value of an unknown angle given the sum of adjacent angles?
3. How do you approach solving equations with multiple terms and variables?
4. What could be other interpretations of Problem 2 based on the layout?
5. How might arithmetic operations in a puzzle be arranged for more complex problem-solving?

Tip:

When solving geometric problems involving angles, always check whether you're dealing with supplementary, complementary, or adjacent angles, as their relationships are key to forming equations.