Which of the following rigid motions is used to prove that vertical angle pairs are congruent? (1) a rotation by 90 about the intersection of the lines creating the vertical angles (2) a rotation by 180 about the intersection of the lines creating the vertical angles (3) a translation in the direction of one of the lines creating the vertical angles (4) a reflection across one of the lines creating the vertical angles

(2) a rotation by about the intersection of the lines creating the vertical angles.

Step-by-step explanation:

Rigid motion are a set of transformation procedure to change the dimension, orientation or size of a given figure or shape. It involves rotation, translation, reflection and dilation.

Vertical angles are formed when two straight lines intersect to form angles. But two opposite angles called vertical angles are equal. To prove that vertical angles are equal; a rotation by about the intersection of the lines creating the vertical angles is required.

45

step-by-step explanation:

30+15

$12. that is my answer.