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
Related questions
Question
![### Geometry Problem: Finding Angle Measures
#### Problem Statement:
**Find \( m\angle Q \):**
The diagram is not to scale.
#### Diagram Description:
The diagram illustrates the crossing of two lines, forming several angles.
1. There are two intersecting lines, one horizontal and one oblique.
2. One of the angles at the intersection is labeled as \( 77^\circ \).
3. Another angle, directly opposite to the oblique line's acute angle, is labeled as \( 47^\circ \).
#### Provided Options:
- \( 124 \)
- \( 103 \)
- \( 56 \)
- \( 66 \)
#### Explanation:
Given the angles \( 77^\circ \) and \( 47^\circ \), you need to determine the measure of \( m\angle Q \).
Let's calculate:
Since the angles on a straight line add up to \( 180^\circ \):
1. Find the supplementary angle to \( 77^\circ \) (since they form a straight line):
\[ 180^\circ - 77^\circ = 103^\circ \]
Considering the labeled angles directly:
- \( 77^\circ \) and the opposite angle makes \( \angle Q \).
Thus, \( m \angle Q = 103^\circ\).
**Correct Answer:** \( 103 \)
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ea68db9-9ac9-4be2-a7e0-76da98d9ee5e%2F1c1fb122-7a74-4d0d-a554-5ab33c073aae%2Ftr5z6j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry Problem: Finding Angle Measures
#### Problem Statement:
**Find \( m\angle Q \):**
The diagram is not to scale.
#### Diagram Description:
The diagram illustrates the crossing of two lines, forming several angles.
1. There are two intersecting lines, one horizontal and one oblique.
2. One of the angles at the intersection is labeled as \( 77^\circ \).
3. Another angle, directly opposite to the oblique line's acute angle, is labeled as \( 47^\circ \).
#### Provided Options:
- \( 124 \)
- \( 103 \)
- \( 56 \)
- \( 66 \)
#### Explanation:
Given the angles \( 77^\circ \) and \( 47^\circ \), you need to determine the measure of \( m\angle Q \).
Let's calculate:
Since the angles on a straight line add up to \( 180^\circ \):
1. Find the supplementary angle to \( 77^\circ \) (since they form a straight line):
\[ 180^\circ - 77^\circ = 103^\circ \]
Considering the labeled angles directly:
- \( 77^\circ \) and the opposite angle makes \( \angle Q \).
Thus, \( m \angle Q = 103^\circ\).
**Correct Answer:** \( 103 \)
---
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