The number of 90° angles formed by the intersections of
E
F
―
and the two parallel lines
A
B
―
and
C
D
―
is
four.
The number of 90° angles formed by the intersections of EF― and the two parallel lines AB― and CD― is dependent on the intersections of EF― with AB― and CD―.
If EF― intersects AB― and CD― at different points, then a total of 4 90° angles are formed - 2 angles at the intersection with AB― and 2 angles at the intersection with CD―.
If EF― intersects AB― and CD― at the same point, then only 2 90° angles are formed - 2 angles at the common intersection point.
Therefore, the number of 90° angles formed can be either 2 or 4, depending on the specific configuration of the lines EF―, AB―, and CD―.
To determine the number of 90° angles formed by the intersections of EF― and the two parallel lines AB― and CD―, we need to consider the properties of parallel lines and transversals.
When two parallel lines, such as AB― and CD―, are intersected by a transversal, such as EF―, several pairs of corresponding angles are formed. One of these pairs is known as the alternate interior angles.
Alternate interior angles are pairs of angles that lie on opposite sides of the transversal, between the two parallel lines. When a transversal intersects parallel lines, alternate interior angles are congruent (equal).
In the case of EF― intersecting AB― and CD―, we can see that four pairs of alternate interior angles are formed.
Let's count the 90° angles formed by the intersections of EF―, AB―, and CD―. Each pair of alternate interior angles can potentially contain a 90° angle. So, if all four pairs are 90° angles, there would be a total of four 90° angles formed.
However, it is important to note that we do not have enough information to determine whether each pair of alternate interior angles is 90°. Therefore, without additional information or measurements, we cannot determine the exact number of 90° angles formed by the intersections of EF―, AB―, and CD―.