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The diagram shows two intersecting lines, forming angles at the intersection point. The given angle is \( 71^\circ \), and the angle \( y \) is directly opposite to it.

Since the lines intersect, they form vertical (opposite) angles, which are always equal.

Therefore:
\[
y = 71^\circ
\]

Vertical angles are congruent, meaning that \( y \) has the same value as the given angle.

Would you like me to provide more details or do you have any questions?

Here are 5 related questions to expand your understanding:

1. What are complementary angles and how are they different from vertical angles?
2. What is the value of the sum of angles that form a straight line?
3. How can you determine if two angles are supplementary or complementary?
4. What property do adjacent angles formed by intersecting lines have?
5. Can you explain the concept of alternate interior angles in parallel lines?

**Tip:** Vertical angles are always equal, and this property can be useful in many geometric proofs and problems involving intersecting lines.

Understand how to find the value of vertical angles using the Vertical Angles Theorem. In this example, y is directly opposite to a 71° angle, making y equal to 71°. Suitable for students in Grades 6-8.

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