Use the image to answer the question.
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.
Which angle is a vertical angle with ∠7 ?
(1 point)
The angle that is vertical to ∠7 is ∠5.
proof
To prove that ∠5 is vertical to ∠7, we need to show that they are formed by intersecting lines and are congruent.
From the given information, we know that angles 5 and 8 are opposite each other. This means that they are formed by intersecting lines and share a vertex.
Additionally, angles 8 and 7 are complementary. This means that they add up to 90 degrees.
Now, if we consider the lines forming angles 7 and 5, we can see that they are parallel slanting lines intersected by a transversal (the horizontal line). According to the properties of parallel lines, alternate interior angles are congruent.
Since angles 8 and 7 are supplementary, it follows that angles 8 and 5 (which are alternate interior angles) are congruent.
Therefore, ∠5 is vertical to ∠7 because they are formed by intersecting lines and are congruent.