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If MO bisects angle L M N, find the value of x. which is the right answer 15,20,25,5

The problem states that line \( MO \) bisects angle \( LMN \), which means the two angles formed on either side of \( MO \) are equal.

From the diagram:

- Angle \( LMO \) is given as \( (x - 60)^\circ \).
- Angle \( O MN \) is given as \( (5x - 80)^\circ \).

Since \( MO \) bisects \( \angle LMN \), these two angles must be equal. Therefore, we can set up the following equation:

\[
(x - 60) = (5x - 80)
\]

### Solving for \( x \):
1. Start by simplifying the equation:
   \[
   x - 60 = 5x - 80
   \]
2. Move all terms involving \( x \) to one side:
   \[
   x - 5x = -80 + 60
   \]
   \[
   -4x = -20
   \]
3. Divide both sides by -4:
   \[
   x = \frac{-20}{-4} = 5
   \]

Thus, the value of \( x \) is **5**.

Would you like more details or have any questions about this solution?

Here are some related questions you might find helpful:
1. How do we verify that the angle bisector divides the angle into equal parts?
2. Can we solve a similar problem with different angle expressions?
3. What happens if the bisector divides the angle into unequal parts?
4. How would the solution change if the terms of the angles were altered?
5. What geometric properties define an angle bisector?

**Tip**: Always check for bisector-related properties when working with angle bisection problems.

If MO bisects angle L M N, find the value of x. Which is the right answer: 15, 20, 25, or 5?

Solve a geometry problem where MO bisects angle LMN. Learn how to set up and solve the equation (x - 60) = (5x - 80) to find the correct value of x. Suitable for students in Grades 9-10.

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