Math / Geometry

Question $\begin{array}{l}m \angle J= \\ m \angle L= \\ m \angle M=\end{array}$

Studdy Solution

STEP 1

1. $JKLM$ is a trapezoid with $JK \parallel ML$ .
2. The sum of interior angles in any quadrilateral is $360^\circ$ .
3. The consecutive angles between the parallel sides of a trapezoid are supplementary.

STEP 2

1. Identify known angles and relationships.
2. Calculate the measure of angle $\angle J$ .
3. Calculate the measure of angle $\angle L$ .
4. Calculate the measure of angle $\angle M$ .

STEP 3

Identify the known angle: $\angle K = 83^\circ$ .

STEP 4

Since $JK \parallel ML$ , angles $\angle K$ and $\angle L$ are consecutive interior angles and are supplementary. Therefore, we have:
$m \angle K + m \angle L = 180^\circ$
Substitute the known value:
$83^\circ + m \angle L = 180^\circ$

STEP 5

Solve for $m \angle L$ :
$m \angle L = 180^\circ - 83^\circ$ $m \angle L = 97^\circ$

STEP 6

Since $JK \parallel ML$ , angles $\angle J$ and $\angle M$ are also consecutive interior angles and are supplementary. Therefore, we have:
$m \angle J + m \angle M = 180^\circ$

STEP 7

Using the property of the sum of interior angles of a quadrilateral, we have:
$m \angle J + m \angle K + m \angle L + m \angle M = 360^\circ$
Substitute the known values:
$m \angle J + 83^\circ + 97^\circ + m \angle M = 360^\circ$

STEP 8

Simplify and solve for $m \angle J + m \angle M$ :
$m \angle J + m \angle M = 360^\circ - 180^\circ$ $m \angle J + m \angle M = 180^\circ$

STEP 9

Since $m \angle J + m \angle M = 180^\circ$ and they are supplementary, we can choose any value for one and solve for the other. However, without additional information, we cannot uniquely determine $m \angle J$ and $m \angle M$ individually.
The measures of the angles are: $m \angle J + m \angle M = 180^\circ$ $m \angle L = 97^\circ$

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