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°".

Answered: If m || n, which statement is true?

Math

Geometry

If m || n, which statement is true?

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

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 supplementary
4. $ 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.

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