https://file.aiquickdraw.com/mathbot/file/1726856335812u6ha9ea4.jpg

In this image, the problem is asking to solve for the value of \( p \). The diagram shows two intersecting lines with angles labeled as \( 104^\circ \) and \( (2p)^\circ \). 

Since the two angles are on a straight line, they form a linear pair, which means they are supplementary. The sum of the angles on a straight line is always \( 180^\circ \).

We can set up the equation as:
\[
104^\circ + (2p)^\circ = 180^\circ
\]

### Step-by-Step Solution:
1. Subtract \( 104^\circ \) from both sides:
   \[
   2p = 180^\circ - 104^\circ
   \]
   \[
   2p = 76^\circ
   \]

2. Divide by 2 to solve for \( p \):
   \[
   p = \frac{76^\circ}{2} = 38^\circ
   \]

Thus, the value of \( p \) is \( 38^\circ \).

Would you like further details on the concepts used here? Here are some related questions you might want to explore:

1. What is the definition of supplementary angles?
2. How do vertical angles relate to intersecting lines?
3. Can linear pairs be unequal in measure?
4. What is the general method to solve for unknowns in geometry?
5. How do parallel and transversal lines differ from intersecting lines?

**Tip:** Always remember that angles forming a straight line sum up to \( 180^\circ \), which is crucial for solving many geometric problems involving linear pairs.

Solve for the value of p in the image where two intersecting lines form a linear pair with angles labeled as 104° and (2p)°.

Learn how to solve for the value of p using the concept of linear pairs and supplementary angles. In this geometry problem, we analyze two intersecting lines, calculate the value of p, and explain key theorems. Suitable for students in Grades 7-9.

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