Please help thanks ### Understanding Parallelograms: Calculations of Lengths and Angles**The figure below is a parallelogram. Fill in each indicated measure.**![Parallelogram Diagram](image_url) *(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 $ inches2. **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: \[

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Description: Please help thanks ### Understanding Parallelograms: Calculations of Lengths and Angles**The figure below is a parallelogram. Fill in each indicated measure.**![Parallelogram Diagram](image_url) *(Note: Include the provided image here for visual refe

We will use properties of parallelogram to find missing angles and sides

Answered: The figure below is a parallelogram.…

Math

Geometry

The figure below is a parallelogram. Fill in each indicated measure. K J 26 E 10 in JK M 14 in JI: 48 MZKME MLJIM m/EMΙ

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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### Understanding Parallelograms: Calculations of Lengths and Angles

**The figure below is a parallelogram. Fill in each indicated measure.**

![Parallelogram Diagram](image_url) *(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:
\[

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