in which figure do $\\angle 1$ and $\\angle 2$ represent a pair of alternate exterior angles?
in which figure do $\\angle 1$ and $\\angle 2$ represent a pair of alternate exterior angles?
Answer
Explanation:
Step1: Recall Alternate Exterior Angles Definition
Alternate exterior angles are formed when a transversal crosses two parallel lines. They lie outside the two lines and on opposite sides of the transversal.
Step2: Analyze Each Figure
- Top - Left Figure: Check the positions of ( \angle 1 ) and ( \angle 2 ). ( \angle 1 ) is on the left - outer side and ( \angle 2 ) is on the right - outer side of the two parallel lines (vertical lines) cut by the transversal (horizontal line). They are outside the two vertical lines and on alternate sides of the transversal.
- Top - Right Figure: ( \angle 1 ) and ( \angle 2 ) are on the same side of the transversal and ( \angle 2 ) is between the two vertical lines, so they are not alternate exterior angles.
- Bottom - Left Figure: ( \angle 2 ) is between the two vertical lines, so it's not an exterior angle.
- Bottom - Right Figure: ( \angle 1 ) and ( \angle 2 ) are on the same side of the transversal and ( \angle 1 ) is between the two vertical lines (or in a position that doesn't fit alternate exterior angles).