https://file.aiquickdraw.com/mathbot/file/1725506270270te15a8dw.jpg

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!

Solve for the missing parts of the diagram. Given: ∠BAE = (x + 9)°, ∠BAD = (3x - 2)°

Learn how to solve for missing angles in a geometric figure where adjacent angles on a straight line are supplementary. This problem involves solving the equation (x + 9)° + (3x - 2)° = 180°, resulting in x = 43.25. Suitable for students in Grades 8-10.

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