The question presented is: "If line \( m \parallel n \), which statement is true?"The image shows two parallel lines, \( m \) and \( n \), cut by a transversal. The transversal intersects lines \( m \) and \( n \), creating various angles labeled as \( a, b, c, d, e, f, \) and \( g \). One of these angles is marked with a measure of \( 121^\circ \).### Diagram Explanation:- **Lines \( m \) and \( n \)**: These are parallel lines, indicated by the notation \( m \parallel n \).- **Transversal**: A line that crosses both parallel lines, forming several angles at the points of intersection.- **Angles**: - **\( a, b, c, d, e, f, \) and \( g \)**: These angles are formed by the intersection of the transversal with lines \( m \) and \( n \). - **Angle \( d \)**: Specifically marked as \( 121^\circ \).### Observations:- Since lines \( m \) and \( n \) are parallel, the following pairs of angles are congruent: - Corresponding angles (e.g., \( a \) and \( c \), \( b \) and \( d \), etc.). - Alternate interior angles (e.g., \( f \) and \( d \)). - Alternate exterior angles. - Consecutive interior angles are supplementary (their sum is \( 180^\circ \)).Given these relationships, the correct statement regarding the truth of the angle parameters can be inferred based on the properties of parallel lines and the transversal. The image shows a diagram of two intersecting lines, creating several angles labeled as follows: - The lines create angles a, b, c, d, e, f, and g.- Angle c is given as 121°.- The lines intersect at a common point forming a vertical angle pair and are extended to show each angle clearly.Below the diagram, there are multiple-choice questions:1. \( m \angle c = 59^\circ \)2. \( m \angle e = 121^\circ \)3. Vertical angles are supplementary4. \( m \angle f = 121^\circ \) The correct answer seems to be identifying angle e as being vertically opposite to angle c, implying \( m \angle e = 121^\circ \).In geometry, vertical angles are congruent, meaning angles directly across from each other when two lines intersect are equal in measure.

Given Data: Parallel lines: m∥n There are two lines m and n parallel to each other and a transversal line which form a, b, c, d, e, f, g, 121°. For the statement "m∠c=59°", The angles ∠c and 121° are a pair of vertical angles. The vertical angles are congruent. So, m∠c=121° Thus, the statement is "m∠c=59°" not true.For the statement "m∠e=121°", The angle g and 121° is a linear pair. The angle g is, m∠g+121°=180°m∠g=180°-121°m∠g=59° The angle g and e is a pair of the corresponding angle, which are congruent. So, m∠e=59° Thus, the statement "m∠e=121°" is not true.For the statement "Vertical angles are supplementary" The vertical angles are c and 121°, so m∠c=121° The supplementary angle must sum up to 180°. For angle c and 121° (Vertical angles) m∠c+121°=121°+121°=242°≠180° Thus, the statement "Vertical angles are supplementary" is not true.For the statement "m∠f=121°", From the figure, the angles f and 121° are corresponding angles. The corresponding angles are always congruent. So, m∠f=121° Thus, the statement "m∠f=121°" is true. Thus, the true statement among the given statement is "m∠f=121°".