Decide whether pairs of angles angle1 and angle2; angle E and angle1. and angle5 and angle6 are alternate interior angles, same-side interior angles, corresponding angles or alternate exterior angles Choose the statement that correctly describes angles 1 and 2 Angles 1 and 2 are alternate exterior angles B. Angles 1 and 2 are same- side interior angles Angles 1 and 2 are alternate interior angles D. Angles 1 and 2 are corresponding angles
The correct statement is:
C. Angles 1 and 2 are alternate interior angles
To determine the relationship between angles 1 and 2, we need to understand the different types of angle relationships.
1. Alternate Interior Angles: These angles are found between two parallel lines and on opposite sides of a transversal. They are equal in measure.
2. Same-Side Interior Angles: These angles are also found between two parallel lines and on the same side of a transversal. They are supplementary, meaning their measures add up to 180 degrees.
3. Corresponding Angles: These angles are found between two parallel lines and on the same side of a transversal. They are equal in measure.
4. Alternate Exterior Angles: These angles are found between two parallel lines and on opposite sides of a transversal. They are equal in measure.
In this case, we are looking at angles 1 and 2. Since they are found between two parallel lines (angle E and angle 1), we can immediately eliminate same-side interior angles and corresponding angles.
Therefore, the correct answer is:
Angles 1 and 2 are alternate interior angles.
To determine the relationship between angle1 and angle2, we need to understand the properties of alternate interior angles, same-side interior angles, corresponding angles, and alternate exterior angles.
Alternate interior angles: These are angles that are on opposite sides of the transversal and inside (between) the two lines being intersected. In other words, if we have two parallel lines intersected by a transversal, alternate interior angles are formed. Angles 1 and 2 are alternate interior angles if they meet these conditions.
Same-side interior angles: These are angles that are on the same side of the transversal and inside (between) the two lines being intersected. In other words, if we have two parallel lines intersected by a transversal, same-side interior angles are formed.
Corresponding angles: These are angles that are in the same position at each intersection. For example, if we have two parallel lines intersected by a transversal, the angle that is above and to the left of angle 1 would be the corresponding angle to angle 1.
Alternate exterior angles: These are angles that are on opposite sides of the transversal and outside (not between) the two lines being intersected. In other words, if we have two parallel lines intersected by a transversal, alternate exterior angles are formed.
By analyzing the question, we can see that angle1 and angle2 are given. Since they are both on the same side of the transversal and inside the intersected lines, they cannot be alternate exterior angles. Therefore, we can eliminate option A.
Since angle1 and angle2 are on the same side of the transversal, they are not same-side interior angles. Therefore, we can eliminate option B.
Since angle1 and angle2 are on opposite sides of the transversal and inside the intersected lines, they are alternate interior angles. Therefore, the correct option is C. Angles 1 and 2 are alternate interior angles.