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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What is is mXW^ based on the figure shown? Assume YW¯is a diameter of the
Transcribed Image Text:The image displays a multiple-choice question with four options, each preceded by a circle indicating a selectable answer. The options are:
- 120°
- 42°
- 60°
- 78°
Each angle is listed vertically, aligned to the right of its corresponding circle.
![**Problem Statement:**
What is \( m \angle XMW \) based on the figure shown? Assume \( \overline{YW} \) is a diameter of the circle.
**Diagram Description:**
The image shows a circle with a diameter \( \overline{YW} \). The diameter divides the circle into two semicircles. Inside the circle, there is a central point labeled \( M \) from which several radii extend to the circumference at points \( Y, D, X, \) and \( W \).
**Angle Details:**
- The angle \( \angle YMD \) measures \( 78^\circ \).
- The angle \( \angle DMX \) measures \( 42^\circ \).
Since \( \overline{YW} \) is a diameter, it splits the circle into two semicircles, making the central angle \( \angle YMW \) equal to \( 180^\circ \).
**Calculation:**
To find \( m \angle XMW \), first find the sum of the known angles:
\[
m \angle YMD + m \angle DMX = 78^\circ + 42^\circ = 120^\circ
\]
Next, subtract this sum from \( 180^\circ \) to find \( m \angle XMW \):
\[
m \angle XMW = 180^\circ - 120^\circ = 60^\circ
\]
Thus, the measure of \( \angle XMW \) is \( 60^\circ \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F081dc05e-0bfb-4e54-b2bd-95ea18e8057c%2Fa83c3a8c-6460-4bbd-b151-b36ce33d9a70%2Fhbbc6vf_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
What is \( m \angle XMW \) based on the figure shown? Assume \( \overline{YW} \) is a diameter of the circle.
**Diagram Description:**
The image shows a circle with a diameter \( \overline{YW} \). The diameter divides the circle into two semicircles. Inside the circle, there is a central point labeled \( M \) from which several radii extend to the circumference at points \( Y, D, X, \) and \( W \).
**Angle Details:**
- The angle \( \angle YMD \) measures \( 78^\circ \).
- The angle \( \angle DMX \) measures \( 42^\circ \).
Since \( \overline{YW} \) is a diameter, it splits the circle into two semicircles, making the central angle \( \angle YMW \) equal to \( 180^\circ \).
**Calculation:**
To find \( m \angle XMW \), first find the sum of the known angles:
\[
m \angle YMD + m \angle DMX = 78^\circ + 42^\circ = 120^\circ
\]
Next, subtract this sum from \( 180^\circ \) to find \( m \angle XMW \):
\[
m \angle XMW = 180^\circ - 120^\circ = 60^\circ
\]
Thus, the measure of \( \angle XMW \) is \( 60^\circ \).
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