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
Topic Video
Question
100%
Solve for a, b, c, and d.
![The image features a geometrical diagram of a quadrilateral inscribed in a circle. Here is a detailed transcription and explanation suitable for an educational website:
**Transcription:**
The diagram consists of:
1. A circle with four points (corners of the quadrilateral) labeled as a°, b°, c°, and d°.
2. A quadrilateral inscribed within the circle, having internal angles marked as 115°, 93°, and 97°.
3. The center of the circle is marked with a small black dot.
4. The vertices of the quadrilateral touch the circumference of the circle.
**Detailed Explanation:**
The image illustrates a quadrilateral inscribed within a circle, highlighting the concept of cyclic quadrilaterals where the vertices lie on the circumference of the circle. In such a quadrilateral, the sum of the opposite angles is always 180 degrees. This property can be used to determine the measures of the angles if some angles are known.
- The quadrilateral has angles:
- One angle measuring 115°
- Adjacent to it, another angle measuring 93°
- The third angle is labeled 97°
To find the fourth angle (denoted as d° in the image), you can use the property of cyclic quadrilaterals where the opposite angles add up to 180°.
- Let the fourth angle be x.
- Sum of angles opposite the 115° and x: 115° + x = 180°
- Sum of angles opposite the 97° and 93°: 97° + 93° = 180°
Thus, x can be solved as:
\[ x = 180° - 115° \]
\[ x = 65° \]
By observing and calculating these angles, one can verify and solidify their understanding of cyclic quadrilaterals and their properties. This exercise is beneficial for learning angle relationships in polygons and especially for understanding properties inherent to cyclic quadrilaterals.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fced4a497-122b-4daf-b2c3-a14b208e07b3%2Fad64a195-7d03-4ac1-87d9-939156d8049b%2F5lvmy7f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image features a geometrical diagram of a quadrilateral inscribed in a circle. Here is a detailed transcription and explanation suitable for an educational website:
**Transcription:**
The diagram consists of:
1. A circle with four points (corners of the quadrilateral) labeled as a°, b°, c°, and d°.
2. A quadrilateral inscribed within the circle, having internal angles marked as 115°, 93°, and 97°.
3. The center of the circle is marked with a small black dot.
4. The vertices of the quadrilateral touch the circumference of the circle.
**Detailed Explanation:**
The image illustrates a quadrilateral inscribed within a circle, highlighting the concept of cyclic quadrilaterals where the vertices lie on the circumference of the circle. In such a quadrilateral, the sum of the opposite angles is always 180 degrees. This property can be used to determine the measures of the angles if some angles are known.
- The quadrilateral has angles:
- One angle measuring 115°
- Adjacent to it, another angle measuring 93°
- The third angle is labeled 97°
To find the fourth angle (denoted as d° in the image), you can use the property of cyclic quadrilaterals where the opposite angles add up to 180°.
- Let the fourth angle be x.
- Sum of angles opposite the 115° and x: 115° + x = 180°
- Sum of angles opposite the 97° and 93°: 97° + 93° = 180°
Thus, x can be solved as:
\[ x = 180° - 115° \]
\[ x = 65° \]
By observing and calculating these angles, one can verify and solidify their understanding of cyclic quadrilaterals and their properties. This exercise is beneficial for learning angle relationships in polygons and especially for understanding properties inherent to cyclic quadrilaterals.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 4 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning