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
Please help thanks
 *(Note: Include the provided image here for visual reference.)*
1. **Given Values:**
- \( \angle JIK = 26^\circ \)
- \( \angle KIM = 48^\circ \)
- Length \( IM = 14 \) inches
- Length \( KM = 10 \) inches
2. **Required Measures:**
- Length \( JK \)
- Length \( JI \)
- Measure \( m \angle KME \)
- Measure \( m \angle JIM \)
- Measure \( m \angle EMI \)
3. **Explanation of the Diagram:**
- Points \( J, K, I, \) and \( M \) form the vertices of a parallelogram.
- Point \( E \) appears to be an intersection of diagonals within the parallelogram.
- Angles and side lengths needed for calculation are marked within the diagram.
4. **Calculation Steps:**
- **Step 1:** *Determine Length \( JK \):*
Since opposite sides of a parallelogram are equal:
\[ \text{JK} = \text{IM} = 14 \text{ inches} \]
- **Step 2:** *Determine Length \( JI \):*
Similarly,
\[ \text{JI} = \text{KM} = 10 \text{ inches} \]
- **Step 3:** *Measure \( m \angle KME \):*
As diagonals in parallelograms bisect each other and opposite angles are equal, calculate:
\[ \angle KME = \angle KIM = 48^\circ \]
- **Step 4:** *Measure \( m \angle JIM \):*
Angles around point \( I \) that include:
\[ \angle JIM = 180^\circ - \angle JIK = 180^\circ - 26^\circ = 154^\circ \]
- **Step 5:** *Measure \( m \angle EMI \):*
Opposite angles in parallelograms are equal:
\[](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbeba505c-351b-4c3a-9c6b-c6e43d7be92f%2Fc4668656-a06d-4dcd-afeb-8ec0f223056f%2Fb24wxmo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Parallelograms: Calculations of Lengths and Angles
**The figure below is a parallelogram. Fill in each indicated measure.**
 *(Note: Include the provided image here for visual reference.)*
1. **Given Values:**
- \( \angle JIK = 26^\circ \)
- \( \angle KIM = 48^\circ \)
- Length \( IM = 14 \) inches
- Length \( KM = 10 \) inches
2. **Required Measures:**
- Length \( JK \)
- Length \( JI \)
- Measure \( m \angle KME \)
- Measure \( m \angle JIM \)
- Measure \( m \angle EMI \)
3. **Explanation of the Diagram:**
- Points \( J, K, I, \) and \( M \) form the vertices of a parallelogram.
- Point \( E \) appears to be an intersection of diagonals within the parallelogram.
- Angles and side lengths needed for calculation are marked within the diagram.
4. **Calculation Steps:**
- **Step 1:** *Determine Length \( JK \):*
Since opposite sides of a parallelogram are equal:
\[ \text{JK} = \text{IM} = 14 \text{ inches} \]
- **Step 2:** *Determine Length \( JI \):*
Similarly,
\[ \text{JI} = \text{KM} = 10 \text{ inches} \]
- **Step 3:** *Measure \( m \angle KME \):*
As diagonals in parallelograms bisect each other and opposite angles are equal, calculate:
\[ \angle KME = \angle KIM = 48^\circ \]
- **Step 4:** *Measure \( m \angle JIM \):*
Angles around point \( I \) that include:
\[ \angle JIM = 180^\circ - \angle JIK = 180^\circ - 26^\circ = 154^\circ \]
- **Step 5:** *Measure \( m \angle EMI \):*
Opposite angles in parallelograms are equal:
\[
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 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