Question

Angle2 = angle ___because their corresponding angles of parallel lines cut by traversal

angle 5= angle ___ by the vertical angles theorem

Answer 1

Angle2 = angle _6__because their corresponding angles of parallel lines cut by traversal

Angle 5 =angle 8 by vertical angle theorem.

Explanation:

Corresponding angles:

If two lines are parallel and a transversal intersect at two points of the parallel lines then we have corresponding angles are equal.

In the figure the corresponding pair angles given below are equal :

angle 2 and angle 6

angle 4 and angle 8

angle 1 and angle 5

angle 3 and angle 7

Vertical angle theorem:

If two lines intersect each other then vertical opposite angles are equal.

In the figure the pair of vertical angles which are equal are

angle 2 and angle 3

angle 1 and angle 4

angle 5 and angle 8

angle 6 and angle 7

Angle2 = angle _6__because their corresponding angles of parallel lines cut by traversal

Angle 5 =angle 8 by vertical angle theorem.