In this figure, lines 1 and 2 are parallel, and lines 3 and l4 are parallel. What is the measure of Lx? A. 50° B. 60° C. 120° 120° Not enough information is provided. Ato z180
In this figure, lines 1 and 2 are parallel, and lines 3 and l4 are parallel. What is the measure of Lx? A. 50° B. 60° C. 120° 120° Not enough information is provided. Ato z180
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter9: Real Numbers And Right Triangles
Section9.5: The Distance And Midpoint Formulas
Problem 2C
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Question
![**Geometry Problem: Parallel Lines and Angles**
**Problem Statement:**
In this figure, lines \( l_1 \) and \( l_2 \) are parallel, and lines \( l_3 \) and \( l_4 \) are parallel. What is the measure of \( \angle x \)?
**Answer Choices:**
A. \( 50^\circ \)
B. \( 60^\circ \)
C. \( 120^\circ \)
D. Not enough information is provided.
**Explanation of Diagram:**
The diagram shows two pairs of parallel lines intersecting each other. Lines \( l_1 \) and \( l_2 \) are parallel and horizontal, while lines \( l_3 \) and \( l_4 \) are also parallel and slanting downwards from left to right.
- There is an angle marked \( 120^\circ \) at one of the intersections.
- In one of the areas of intersection, angles \( y \) and \( x \) are indicated but not labeled with their measures.
- An additional note indicates that the sum of angles \( \Delta \) and \( o \) equals \( 180 \) degrees: \( \Delta + o = 180 \).
Considering the parallel lines and the noted angle of \( 120^\circ \), the angle \( x \) can be deduced using angle relationships such as alternate interior angles, corresponding angles, or supplementary angles.
**Solution:**
Since lines \( l_3 \) and \( l_4 \) are parallel and a transversal cuts across them, angle \( x \) is supplementary to the given angle of \( 120^\circ \) (as they lie on a straight line).
Therefore:
\[
\angle x + 120^\circ = 180^\circ
\]
\[
\angle x = 180^\circ - 120^\circ
\]
\[
\angle x = 60^\circ
\]
Thus, the correct answer is:
**B. \( 60^\circ \)**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5b4de2cd-a567-4373-911c-936e397ded87%2F1503004a-1d5b-48cf-91d7-be84c0cd9104%2Fcf9dfjj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Geometry Problem: Parallel Lines and Angles**
**Problem Statement:**
In this figure, lines \( l_1 \) and \( l_2 \) are parallel, and lines \( l_3 \) and \( l_4 \) are parallel. What is the measure of \( \angle x \)?
**Answer Choices:**
A. \( 50^\circ \)
B. \( 60^\circ \)
C. \( 120^\circ \)
D. Not enough information is provided.
**Explanation of Diagram:**
The diagram shows two pairs of parallel lines intersecting each other. Lines \( l_1 \) and \( l_2 \) are parallel and horizontal, while lines \( l_3 \) and \( l_4 \) are also parallel and slanting downwards from left to right.
- There is an angle marked \( 120^\circ \) at one of the intersections.
- In one of the areas of intersection, angles \( y \) and \( x \) are indicated but not labeled with their measures.
- An additional note indicates that the sum of angles \( \Delta \) and \( o \) equals \( 180 \) degrees: \( \Delta + o = 180 \).
Considering the parallel lines and the noted angle of \( 120^\circ \), the angle \( x \) can be deduced using angle relationships such as alternate interior angles, corresponding angles, or supplementary angles.
**Solution:**
Since lines \( l_3 \) and \( l_4 \) are parallel and a transversal cuts across them, angle \( x \) is supplementary to the given angle of \( 120^\circ \) (as they lie on a straight line).
Therefore:
\[
\angle x + 120^\circ = 180^\circ
\]
\[
\angle x = 180^\circ - 120^\circ
\]
\[
\angle x = 60^\circ
\]
Thus, the correct answer is:
**B. \( 60^\circ \)**
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