Question

juan decided to test what would happen if he rotated an angle. homework help
a. he copied the angle at right on tracing paper and rotated it 180° about its vertex. what type of angle pair did he
create? what is the relationship of these angles?
b. juan then rotated the same angle 180° through a different point (see the diagram at right). on your paper, draw
juans angle and the rotated image. describe the overall shape formed by the two angles.

Explanation:

a.

When an angle is rotated \(180^{\circ}\) about its vertex, the two angles (the original and the rotated one) form a linear pair. A linear pair of angles is adjacent angles that are supplementary (their sum is \(180^{\circ}\)). Also, they are vertical angles (opposite angles formed by two intersecting lines), and vertical angles are congruent.

When an angle is rotated \(180^{\circ}\) about a non - vertex point, the two angles (the original and the rotated one) form a parallelogram - like shape. If we consider the sides of the angles as line segments, the opposite sides of the figure formed by the two angles are parallel.

Answer:

He created a linear pair (and also vertical angles). The angles are supplementary (for the linear - pair aspect) and congruent (for the vertical - angles aspect).

b.