From the image, we have a geometric figure showing angles related to a quadrilateral with the following given information:

• $\angle BAE = (x + 9)^\circ$
• $\angle BAD = (3x - 2)^\circ$

You are asked to solve for the missing parts of the diagram.

Since $\angle BAE$ and $\angle BAD$ are adjacent angles that form a straight line (which is 180°), the equation we can form is: $(x + 9)^\circ + (3x - 2)^\circ = 180^\circ$

Now, we will solve this equation:

1. Combine like terms: $x + 9 + 3x - 2 = 180$ $4x + 7 = 180$

2. Subtract 7 from both sides: $4x = 173$

3. Divide by 4: $x = \frac{173}{4} = 43.25$

Now that we know $x = 43.25$, we can substitute this value back into the expressions for the angles to find their measures:

• $\angle BAE = (x + 9) = 43.25 + 9 = 52.25^\circ$
• $\angle BAD = (3x - 2) = 3(43.25) - 2 = 129.75 - 2 = 127.75^\circ$

Thus, the angles are:

• $\angle BAE = 52.25^\circ$
• $\angle BAD = 127.75^\circ$

Would you like further details on the process or to ask questions?

Here are 5 related questions to expand your understanding:

1. How are adjacent angles on a straight line related to each other?
2. Can you solve a similar problem where the angles are supplementary but not adjacent?
3. How would the problem change if $\angle BAE$ and $\angle BAD$ were complementary instead of supplementary?
4. How do you verify the correctness of the solution for angle measures?
5. What happens to the other angles in a quadrilateral when two angles are known?

Tip: Always double-check whether the angles form a straight line (supplementary) or some other relationship to avoid solving incorrectly!