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To solve for the measure of angle \( O \) in parallelogram \( LMNO \), we will use properties of parallelograms and the given information from the image.

### Step-by-step approach:

1. **Properties of a parallelogram**: In any parallelogram, opposite angles are equal, and adjacent angles are supplementary (they add up to \(180^\circ\)).

2. **Given angles**:
   - Angle \( L \) is \( (x + 40)^\circ \).
   - Angle \( O \) is \( (3x)^\circ \).

3. **Relationship between angles \( L \) and \( O \)**:
   Since \( L \) and \( O \) are adjacent angles in a parallelogram, they must add up to \( 180^\circ \). Therefore, we can write:
   \[
   (x + 40) + (3x) = 180
   \]

4. **Solve for \( x \)**:
   \[
   4x + 40 = 180
   \]
   Subtract 40 from both sides:
   \[
   4x = 140
   \]
   Divide by 4:
   \[
   x = 35
   \]

5. **Find angle \( O \)**:
   Since \( \text{Angle } O = 3x \), substitute \( x = 35 \):
   \[
   \text{Angle } O = 3(35) = 105^\circ
   \]

Thus, the measure of angle \( O \) is **105°**.

Would you like more details or have any questions?

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Here are 5 related questions to extend the problem:

1. What is the measure of angle \( L \)?
2. How do you calculate angle \( M \) in parallelogram \( LMNO \)?
3. What would happen if the values of the angles were swapped?
4. Can you verify if the opposite angles in parallelogram \( LMNO \) are equal?
5. How would you check if the sides of parallelogram \( LMNO \) are congruent?

**Tip**: In any parallelogram, knowing one angle allows you to find all other angles due to symmetry and supplementary relationships!

What is the measure of angle O in parallelogram LMNO?

Discover how to calculate the measure of angle O in parallelogram LMNO using algebra and properties of parallelograms. Follow a step-by-step solution, including solving the equation (x + 40) + 3x = 180 to find angle O as 105°. This problem is suitable for students in Grades 8-10.

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