QUestion15 **Understanding Rigid Motions in Geometry**In the diagram below, a sequence of rigid motions maps the quadrilateral $ABCD$ onto $JKLM$.![Diagram of Rigid Motions](link-to-diagram.png)The diagram features two quadrilaterals on a coordinate plane:1. Quadrilateral $ABCD$ positioned in the first quadrant.2. Quadrilateral $JKLM$ positioned in the third quadrant.### Axes:- **X-axis**: Horizontal axis of the coordinate plane- **Y-axis**: Vertical axis of the coordinate plane### Vertices:- **$ABCD$**: - $A$ is positioned at top right. - $B$ is located slightly below and to the left of $A$. - $C$ is below $B$. - $D$ is to the right of $C$.- **$JKLM$**: - $J$ is positioned to the top right. - $K$ is to the left of $J$. - $L$ is below $K$. - $M$ is right of $L$.### Given Angles:- $\angle A = 82^\circ$- $\angle B = 104^\circ$- $\angle L = 121^\circ$### Unknown Angle:- $\angle M$The task is to determine the measure of $\angle M$. Given the angles and the nature of rigid motions, which preserve angles and relative side lengths:- Rigid motions include translations, rotations, and reflections.- The sum of angles in any quadrilateral is $360^\circ$.### Calculation:Sum of angles in $JKLM$:\[ \angle J + \angle K + \angle L + \angle M = 360^\circ \]Given:\[ \angle J \equiv \angle A = 82^\circ \]\[ \angle K \equiv \angle B = 104^\circ \]\[ \angle L = 121^\circ \]To find $\angle M$:\[ 82^\circ + 104^\circ + 121^\circ + \angle M = 360^\circ \]\[ 307^\circ + \angle M = 360^\circ \]\[ \angle M = 360

Name: QUestion15 **Understanding Rigid Motions in Geometry**In the diagram b
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Description: QUestion15 **Understanding Rigid Motions in Geometry**In the diagram below, a sequence of rigid motions maps the quadrilateral $ABCD$ onto $JKLM$.![Diagram of Rigid Motions](link-to-diagram.png)The diagram features two quadrilaterals on a coordin

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Answered: In the diagram below, a sequence of…

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In the diagram below, a sequence of rigid motions maps ABCD onto JKLM. If m Z A= 82°,mZ B= 104°, and m Z L = 121°, the mZ M53 degrees %3D %3D

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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QUestion15

**Understanding Rigid Motions in Geometry**

In the diagram below, a sequence of rigid motions maps the quadrilateral $ABCD$ onto $JKLM$.

![Diagram of Rigid Motions](link-to-diagram.png)

The diagram features two quadrilaterals on a coordinate plane:
1. Quadrilateral $ABCD$ positioned in the first quadrant.
2. Quadrilateral $JKLM$ positioned in the third quadrant.

### Axes:
- **X-axis**: Horizontal axis of the coordinate plane
- **Y-axis**: Vertical axis of the coordinate plane

### Vertices:
- **$ABCD$**:
- $A$ is positioned at top right.
- $B$ is located slightly below and to the left of $A$.
- $C$ is below $B$.
- $D$ is to the right of $C$.
- **$JKLM$**:
- $J$ is positioned to the top right.
- $K$ is to the left of $J$.
- $L$ is below $K$.
- $M$ is right of $L$.

### Given Angles:
- $\angle A = 82^\circ$
- $\angle B = 104^\circ$
- $\angle L = 121^\circ$

### Unknown Angle:
- $\angle M$

The task is to determine the measure of $\angle M$.

Given the angles and the nature of rigid motions, which preserve angles and relative side lengths:
- Rigid motions include translations, rotations, and reflections.
- The sum of angles in any quadrilateral is $360^\circ$.

### Calculation:
Sum of angles in $JKLM$:
\[ \angle J + \angle K + \angle L + \angle M = 360^\circ \]

Given:
\[ \angle J \equiv \angle A = 82^\circ \]
\[ \angle K \equiv \angle B = 104^\circ \]
\[ \angle L = 121^\circ \]

To find $\angle M$:
\[ 82^\circ + 104^\circ + 121^\circ + \angle M = 360^\circ \]
\[ 307^\circ + \angle M = 360^\circ \]
\[ \angle M = 360

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