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
![**Problem:**
Find the measure of the "?" angle.
**Diagram Explanation:**
The diagram consists of two intersecting triangles. Each triangle has its own set of angles.
- One triangle has angles measuring \(22^\circ\) and \(?\).
- The other triangle has angles measuring \(41^\circ\) and \(20^\circ\).
The triangles intersect, sharing the angle marked \(?\).
**Solution:**
To find the measure of the angle marked "?", use the fact that the sum of angles in a triangle is always \(180^\circ\).
1. Calculate the missing angle in the triangle with angles \(41^\circ\) and \(20^\circ\):
\[
41^\circ + 20^\circ + ? = 180^\circ
\]
\[
61^\circ + ? = 180^\circ
\]
\[
? = 180^\circ - 61^\circ = 119^\circ
\]
Therefore, the measure of the "?" angle is \(119^\circ\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6ed396a-58be-4ac0-9d00-206a35697371%2F2499d0b4-aa51-4822-86f9-42c5a8f89454%2F5he1f7v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
Find the measure of the "?" angle.
**Diagram Explanation:**
The diagram consists of two intersecting triangles. Each triangle has its own set of angles.
- One triangle has angles measuring \(22^\circ\) and \(?\).
- The other triangle has angles measuring \(41^\circ\) and \(20^\circ\).
The triangles intersect, sharing the angle marked \(?\).
**Solution:**
To find the measure of the angle marked "?", use the fact that the sum of angles in a triangle is always \(180^\circ\).
1. Calculate the missing angle in the triangle with angles \(41^\circ\) and \(20^\circ\):
\[
41^\circ + 20^\circ + ? = 180^\circ
\]
\[
61^\circ + ? = 180^\circ
\]
\[
? = 180^\circ - 61^\circ = 119^\circ
\]
Therefore, the measure of the "?" angle is \(119^\circ\).
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