Total 8 angles are formed when parallel lines are cut by a transversal.There relationships are mentioned below.
When two lines don't intersect, they are said to be parallel. Parallel lines are two lines that run parallel to each other and meet at infinity.
A transversal is formed when a line intersects two lines at distinct points.
When a transversal intersects two or more parallel lines, various angle pairs are formed. As shown in the figure below, a and d are two parallel lines intersected by the transversal l at the points P and Q.
When a pair of parallel lines is transversally cut, 8 angles are formed, as shown in the figure.
The relationship between the angles are:
pair of angles was formed. Relationships between angles
Corresponding angle pairs. ∠1 = ∠6, ∠4 = ∠8, ∠2 = ∠5, ∠3 = ∠7
Alternate interior angles pairs. ∠4 = ∠5, ∠3 = ∠6
Alternate exterior angle pairs. ∠1 = ∠7, ∠2 = ∠8
Interior angle pairs that are on ∠3 + ∠5 = 180°, ∠4 + ∠6 = 180°
same side of the transversal .
Vertically opposite angle pairs. ∠7 = ∠6, ∠8 = ∠5, ∠1 = ∠3, ∠2 = ∠4,
Thus, total 8 angles are formed when parallel lines are cut by a transversal
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