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The given diagram shows two lines that are parallel, and the angles are expressed algebraically as \(3x^\circ\) and \((5x - 45)^\circ\). These angles are positioned such that they are alternate interior angles, meaning they should be equal due to the properties of parallel lines.

### Step-by-step solution:
1. **Set the two angles equal** because alternate interior angles are congruent:
   \[
   3x = 5x - 45
   \]
   
2. **Solve for \(x\):**
   \[
   3x = 5x - 45
   \]
   Subtract \(3x\) from both sides:
   \[
   0 = 2x - 45
   \]
   Add \(45\) to both sides:
   \[
   45 = 2x
   \]
   Divide by 2:
   \[
   x = 22.5
   \]

3. **Substitute \(x = 22.5\) into the expression for \(\angle 1\)** (which is \(3x^\circ\)):
   \[
   \angle 1 = 3(22.5) = 67.5^\circ
   \]

### Conclusion:
The measure of \(\angle 1\) is \(67.5^\circ\), so the correct answer is **B**.

Would you like more details or have any questions? Here are some related questions to explore:

1. How do alternate interior angles help in solving angle problems with parallel lines?
2. What are other types of angle relationships that occur with parallel lines?
3. How would the solution change if the lines weren't parallel?
4. What is the importance of transversals in geometry?
5. Can you apply these concepts to find unknown angles in different geometric shapes?

**Tip:** Always remember to check if lines are parallel when solving for unknown angles using geometric properties!

In the diagram, two measures of angles are given in algebraic form. Which statement is true about angle 1?

Learn how to solve for angle 1 using the Alternate Interior Angles Theorem. The problem involves algebraic expressions for angles along parallel lines. This step-by-step solution is suitable for students in Grades 8-10.

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