An illustration shows a horizontal line intersecting two parallel slanting lines. The angles the horizontal line forms with left 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 horizontal line forms with right 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 ∠3
?

Answer 1

In geometry, vertical angles are angles that are opposite each other when two lines intersect. From your description, we know that the pairs of angles formed by the horizontal line and the two sets of slanting lines are related.

You mentioned that angles 2 and 3 are opposite each other. Given that, angle 3 will have a vertical angle, which is the angle that is also opposite to it over the point of intersection of the two lines.

Since angles 2 and 3 are formed by the intersection of the horizontal line with the left set of slanting lines, the angle that makes a vertical pair with ∠3 will be ∠6, which is opposite to it on the right side of the diagram.

Thus, the answer is ∠6.