https://file.aiquickdraw.com/mathbot/file/1725468732146uk1xmq8z.jpg

Let's analyze the problem in the image:

The figure \(ABCD\) is a parallelogram. In a parallelogram, opposite angles are equal, and the sum of adjacent angles is \(180^\circ\). 

Given:
- \(\angle DAB = 4p + 12^\circ\)
- \(\angle BCD = 36^\circ\)

Since \(ABCD\) is a parallelogram, the adjacent angles must sum up to \(180^\circ\). Therefore:

\[
\angle DAB + \angle BCD = 180^\circ
\]

Substituting the given values:

\[
(4p + 12^\circ) + 36^\circ = 180^\circ
\]

Simplifying the equation:

\[
4p + 48^\circ = 180^\circ
\]

Subtract \(48^\circ\) from both sides:

\[
4p = 132^\circ
\]

Now, divide by 4:

\[
p = \frac{132^\circ}{4} = 33^\circ
\]

It seems there was a mistake in calculation, let's clarify:
- The correct step would be:
  
  \( 132^\circ / 4 = 33 \)
  
But I notice the answers given in the multiple-choice do not include 33, so let's ensure the setup was correct. 

It appears I made a mistake; I'll recalculate by ensuring the setup:

Given \( 4p + 12^\circ \) and \( 36^\circ \):

\[
(4p + 12^\circ) + 36^\circ = 180^\circ
\]
\[
4p + 48^\circ = 180^\circ
\]
\[
4p = 180^\circ - 48^\circ = 132^\circ
\]
So:
\[
p = 132^\circ / 4 = 33^\circ
]

Rechecking: \( p \) value of 33 is mathematically correct for setup but is a mismatch, possibly something wrong in display. We should inspect the setup data once again.

Would you like to go through the assumptions? 
Now considering adjacent angle context.

1. What is the sum of adjacent angles in parallelogram?
2. Why are alternate angles used in a setup for parallelogram?
3. What concepts connect with side or length in such geometrical shapes?
4. How are supplementary angles used in parallelogram?
5. How does one set equations right in context of problem?

Tip: Ensure the problem type in parallelogram like this examines both steps and context.

Figure ABCD is a parallelogram. Given that ∠DAB = 4p + 12° and ∠BCD = 36°, what is the value of p?

Learn how to solve for the variable p in a parallelogram given the angles ∠DAB = 4p + 12° and ∠BCD = 36°. This problem involves understanding the properties of parallelograms and setting up a linear equation. Suitable for students in Grades 8-10.

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