Question

What reason can be given to show that <4 = <5?

A) They are alternate interior angles formed by a transversal line intersecting two parallel lines.
B) They are vertical angles formed by the intersection of two lines.
C) They are corresponding angles formed by a transversal line intersecting two parallel lines.
D) They are supplementary angles.

Answer 1

Angle <4 and Angle <5 are corresponding angles formed by a transversal line intersecting two parallel lines.

Step-by-step explanation:

The reason that can be given to show that Angle <4 is equal to Angle <5 is option C) They are corresponding angles formed by a transversal line intersecting two parallel lines.

When a transversal line intersects two parallel lines, it creates pairs of congruent angles known as corresponding angles. In this case, Angle <4 and Angle <5 are corresponding angles because they are formed when the transversal line intersects the parallel lines in the same position.

For example, if the lines are marked as m and n and the transversal line as t, Angle <4 is formed when line t intersects line m, and Angle <5 is formed when line t intersects line n. Since these angles are in the same position and intersected by the same transversal line, they are congruent and therefore equal.