Question

Give the most convincing explanation for why the measure of angle

∠A is equal to the measure of angle∠C.
a. By the Vertical Angles Theorem
b. Due to the Corresponding Angles Postulate
c. According to the Alternate Interior Angles Theorem
d. Resulting from the Consecutive Interior Angles Theorem

Answer 1

The measure of angle ∠A is equal to the measure of angle ∠C due to the Vertical Angles Theorem.

Step-by-step explanation:

The most convincing explanation for why the measure of angle ∠A is equal to the measure of angle ∠C is due to the Vertical Angles Theorem. According to this theorem, when two straight lines intersect each other, the opposite (or vertical) angles are equal. This explains why ∠A and ∠C would have the same measurement, and thus option (a) is the correct answer.

The most convincing explanation for why the measure of angle ∠A is equal to the measure of angle ∠C is a. By the Vertical Angles Theorem.

The Vertical Angles Theorem states that when two lines intersect, the vertical angles formed are congruent. In this case, angle ∠A and angle ∠C are formed when line AD intersects line CF. Since they are vertical angles, they must be congruent, and therefore, their measures are equal.

Therefore answer is a. By the Vertical Angles Theorem.