https://file.aiquickdraw.com/mathbot/file/1728591330678sp0h21zh.jpg

This image shows a pair of parallel lines (indicated by the arrows) cut by a transversal line, forming alternate interior angles.

Since the given angle is \(71^\circ\), and angles \(q\) and \(71^\circ\) are alternate interior angles (a property of parallel lines and a transversal), they must be congruent.

Thus, \(q = 71^\circ\).

Would you like further explanation or have any additional questions?

Here are five related questions for further practice:
1. What are corresponding angles, and how do they relate to alternate interior angles?
2. How do you prove that alternate interior angles are congruent using parallel lines?
3. What would happen to the value of \(q\) if the lines were not parallel?
4. How can you find unknown angles when more than two lines are involved?
5. Can alternate exterior angles also be equal in a similar setup? Why?

**Tip:** Always look for congruent angle pairs (alternate interior, corresponding, or vertical) when dealing with parallel lines crossed by a transversal.

Find q, given that the lines are parallel and one angle is 71°.

Solve for angle q using the alternate interior angles theorem with parallel lines and a transversal. In this example, one angle is given as 71°, and the problem involves finding the congruent angle. Suitable for students in Grades 6-8.

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