https://file.aiquickdraw.com/mathbot/file/1727025245427yflpc1r7.jpg

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We are given two intersecting lines, and the measure of one of the angles is \(140^\circ\). Angles \(\angle 1\) and \(\angle 2\) are labeled, and we need to find their measures.

### Step-by-step solution:

1. **Identify angle pairs:**
   - From the diagram, \(\angle 1\) and the \(140^\circ\) angle are **vertical angles**, meaning they are equal. Thus, \[
   m\angle 1 = 140^\circ.
   \]
   
2. **Use the Linear Pair Theorem:**
   - \(\angle 1\) and \(\angle 2\) are adjacent and form a straight line, which means they are supplementary. Therefore, their measures add up to \(180^\circ\).
   - Using this, we can find \(m\angle 2\) as follows: \[
   m\angle 1 + m\angle 2 = 180^\circ,
   \]
   \[
   140^\circ + m\angle 2 = 180^\circ,
   \]
   \[
   m\angle 2 = 180^\circ - 140^\circ = 40^\circ.
   \]

### Final Answer:
- \(m\angle 1 = 140^\circ\)
- \(m\angle 2 = 40^\circ\)

### Theorem used:
- **Vertical Angle Theorem**: Vertical angles are congruent (equal).
- **Linear Pair Theorem**: Adjacent angles that form a straight line are supplementary (add to \(180^\circ\)).

Let me know if you need further details or clarifications. Here are some follow-up questions you can explore:

1. How do we know that vertical angles are always congruent?
2. Can we use any other theorem to find the measure of \(\angle 2\)?
3. What is the difference between vertical and supplementary angles?
4. If the given angle were different, how would that affect the measures of \(\angle 1\) and \(\angle 2\)?
5. What if the lines were not straight? Would these theorems still apply?

**Tip**: Always remember, vertical angles are equal, and adjacent angles on a straight line sum up to \(180^\circ\).

Find m∠1 and m∠2. Tell which theorem can be used.

This problem involves finding the measures of angles ∠1 and ∠2 using the Vertical Angle Theorem and the Linear Pair Theorem. The given angle is 140°, and you will learn how to calculate the adjacent angle. Suitable for students in Grades 7-9.

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