https://file.aiquickdraw.com/mathbot/file/1726224176511ug3hskfy.jpg

In the image, there is a set of intersecting lines, forming angles. One angle is given as \(120^\circ\), and another is expressed as \(2p + 20^\circ\).

We can use the property of vertically opposite angles to solve for \(p\). Vertically opposite angles are equal, so:

\[
2p + 20^\circ = 120^\circ
\]

Now, solving for \(p\):

\[
2p + 20 = 120
\]
\[
2p = 120 - 20
\]
\[
2p = 100
\]
\[
p = \frac{100}{2} = 50
\]

Thus, \(p = 50\).

Would you like more details or have any questions?

Here are some related questions:
1. What are vertically opposite angles?
2. How would the solution change if another angle were given?
3. Can the angle sum property of a straight line be used here?
4. What other properties of intersecting lines are useful for solving such problems?
5. How do you verify if your solution is correct in geometry problems?

**Tip**: Always look for symmetry and equal angles when working with intersecting lines to simplify the problem.

Solve for p in the equation involving vertically opposite angles, where one angle is 120° and the other is expressed as 2p + 20°.

Learn how to solve for p using the property of vertically opposite angles in a geometry problem. This example involves an algebraic expression for one angle, and its solution highlights key concepts in geometry and algebra.

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