Final answer:
The measure of vertical angles adds up to 180 degrees.
Step-by-step explanation:
Vertical angles are formed when two lines intersect. They are equal in measure and are opposite to each other. Given that Z2 and Z4 are vertical angles, we can prove that their measures add up to 180 degrees. Therefore, the correct answer is option a) m2 + m4 = 180.
The question asks to prove certain properties given that Z2 and Z4 are vertical angles. Vertical angles are congruent, which means they have the same measure. This implies that m2 = m4 (where 'm' denotes the measure of the angles). Therefore:
(a) Since Z2 and Z4 form a pair of vertical angles, they sum up to 180 degrees, so m2 + m4 = 180.
(b) As for m2 - m4, since m2 equals m4, their difference would be 0, not 90 degrees.
(c) Again, knowing that vertical angles are equal, m2 x m4 would be m2^2 or m4^2, which doesn't necessarily equal 360.
(d) Since the measures are equal, m2 / m4 would indeed be 1.
The rest of the given information does not apply directly to the question about vertical angles in geometry. Therefore, we can assert that the correct statement is a), m2 plus m4 equals 180 degrees, and d), m2 divided by m4 equals 1.