Final answer:
The correct answer is F. m∠1 ≅ m∠3.
Step-by-step explanation:
Vertical angles are opposite angles formed by intersecting lines, and they are always congruent. In this scenario, ∠1 and ∠3 are vertical angles because they share a common vertex and their sides form two pairs of opposite rays. According to the vertical angle theorem, vertical angles are congruent, meaning that their measures are equal. Therefore, the measure of angle 1 (m∠1) is equal to the measure of angle 3 (m∠3), establishing the congruence between the angles. This relationship between the vertical angles is a property inherent in geometric configurations formed by intersecting lines, ensuring that these angles have identical measures.
The correct choice, F. m∠1 ≅ m∠3, affirms the equality of the measures of ∠1 and ∠3. This conclusion relies on the fundamental principle that vertical angles, formed by the intersection of lines, possess congruent measures. Thus, whenever two angles are recognized as vertical angles, their measures will always be equal, demonstrating the relationship of congruence between these specific pairs of angles. Hence, in the given context, ∠1 and ∠3 are proven to be congruent as they constitute a pair of vertical angles.