https://file.aiquickdraw.com/mathbot/file/17265818030990kw5rumc.jpg

In the image, we see two intersecting lines, creating vertical and adjacent angles. The given angle measures are \(114^\circ\) and \(66^\circ\), and the unknown angle is labeled \(p\).

### Step-by-Step Solution:

1. **Adjacent Angles**: Adjacent angles on a straight line add up to \(180^\circ\).
   - The \(114^\circ\) angle and the unknown angle \(p\) are adjacent.
   - Using the equation: 
   \[
   114^\circ + p = 180^\circ
   \]
   Solving for \(p\):
   \[
   p = 180^\circ - 114^\circ = 66^\circ
   \]

Thus, the unknown angle \(p = 66^\circ\).

### Explanation:
- In this diagram, the two lines intersect at a point, forming vertical angles. Vertical angles are always equal. Therefore, \(p = 66^\circ\) because it is vertically opposite to the given \(66^\circ\) angle.

Would you like more details on this, or do you have any questions?

### Related Questions:
1. What are complementary and supplementary angles?
2. How do you find the measure of vertically opposite angles?
3. How can we identify adjacent angles in more complex geometric figures?
4. What is the sum of angles around a point?
5. Can angles formed by intersecting lines always be equal?

### Tip:
Remember that vertical angles are always congruent, and adjacent angles on a straight line always add up to \(180^\circ\).

What is the value of angle p in the diagram with intersecting lines and given angles 114° and 66°?

Learn how to solve for the unknown angle p using vertical angles and adjacent angle properties. This geometry problem involves a step-by-step solution of angles in intersecting lines. Suitable for middle school students.

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