Two parallel lines cut by a transversal can create all the following types of angles except
A. Alternate interior angles
B. Alternate exterior angles
C. Corresponding angles
D. Complementary angles
I got y’all, it’s all except complementary angles, meaning the answer is D. Trust I’ve gotten this question a few times :)
To find the answer to this question, you need to understand the concepts of parallel lines and transversals.
Parallel lines are lines that are always the same distance apart and never intersect. A transversal is a line that intersects two or more lines at distinct points.
When a transversal intersects two parallel lines, it creates various types of angles. Let's discuss each of the given options to determine which type of angle cannot be created by the intersection of parallel lines with a transversal:
A. Alternate interior angles: These angles are formed on opposite sides of the transversal and inside the parallel lines. For example, if line A and line B are parallel lines, and line C is a transversal intersecting them, then the angles 1 and 5 in the diagram below are alternate interior angles.
```
1 2 3
| | |
Line A -------- Line C ------- Line B
| | |
4 5 6
```
B. Alternate exterior angles: These angles are formed on opposite sides of the transversal and outside the parallel lines. In the same example, the angles 2 and 6 in the diagram above are alternate exterior angles.
C. Corresponding angles: These angles are formed in the same position, relative to the transversal and the parallel lines. For example, angles 1 and 2 in the diagram above are corresponding angles.
D. Complementary angles: Complementary angles are angles that add up to 90 degrees. They can be formed by any two angles as long as their sum is 90 degrees. The intersection of parallel lines with a transversal can create angles that add up to 90 degrees, so complementary angles can be formed in this case.
Based on the above explanations, the answer is D. Complementary angles. All the other options (A, B, and C) can be created by two parallel lines intersected by a transversal, but complementary angles are not restricted to this scenario and can be formed regardless of the intersection of parallel lines.