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21 22 23 24 25 What is the measure of angle $\mathrm{L}$ in parallelogram LMNO? $20^{\circ}$ $30^{\circ}$ $40^{\circ}$ $50^{\circ}$ Mark this and retum Save and Exit Nex: Submit

Asked By WhisperingSkyline26 at

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Charles

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Solution By Steps

Step 1: Identify the properties of a parallelogram

In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (sum to 180°).

Step 2: Set up the equation for supplementary angles

Given angles:

\angle M = 2x

\angle L = 3x - 20°

Since

\angle M and

\angle L are adjacent angles in a parallelogram, they are supplementary:

2x + (3x - 20°) = 180°

Step 3: Solve for

x

Combine like terms:

2x + 3x - 20° = 180°

5x - 20° = 180°

Add 20° to both sides:

5x = 200°

Divide by 5:

x = 40°

Step 4: Calculate

\angle L

Substitute

x = 40° back into the expression for

\angle L:

\angle L = 3x - 20°

\angle L = 3(40°) - 20°

\angle L = 120° - 20°

\angle L = 100°

Final Answer

The measure of angle

L in parallelogram LMNO is

100°.

(Note: The given options do not include 100°, so there might be an error in the problem statement or the provided options.)

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