An illustration shows a slanting line intersecting with two parallel horizontal lines. The angles the slanting line forms with top parallel line are 1, 2, 3, and 4. Angles 1 and 2 are complementary. Angles 2 and 4 are complementary. Angles 4 and 3 are complementary. Angles 3 and 1 are complementary. Angles 1 and 4 are opposite each other. Angles 2 and 3 are opposite each other. The angles the slanting line forms with bottom parallel line are 5, 6, 7, and 8. . Angles 5 and 6 are complementary. Angles 6 and 8 are complementary. Angles 8 and 7 are complementary. Angles 7 and 5 are complementary. Angles 5 and 8 are opposite each other. Angles 6 and 7 are opposite each other.

Question

Which angle makes a vertical pair with ∠5
?

Answer 1

Vertical angles are pairs of opposite angles created when two lines intersect. In your illustration, angles formed at the intersection of the slanting line with the top parallel line are angles 1, 2, 3, and 4, while angles formed at the intersection with the bottom parallel line are angles 5, 6, 7, and 8.

Given that:

• Angles 5 and 8 are opposite each other,
• Angles 6 and 7 are opposite each other,

To find the angle that makes a vertical pair with \( \angle 5 \):

• The vertical angle opposite \( \angle 5 \) is \( \angle 7 \), because they are formed by the intersection of the slanting line and the bottom parallel line.

Thus, the answer is that \( \angle 7 \) makes a vertical pair with \( \angle 5 \).