Question

Rhombus LMNO
has a diagonal line LN¯¯¯¯¯¯¯¯
, and ∠MNL
is 55 degrees. What is m∠MNO
?(1 point) Solve this equation correctly and carefully and tell me how can you get the correct answer for me

Answer 1

To find the measure of angle \( m\angle MNO \) in rhombus \( LMNO \) given that \( \angle MNL = 55^\circ \), we can utilize the properties of a rhombus.

1. **Properties of Rhombus**:
- Opposite angles are equal.
- Adjacent angles are supplementary (their measures add up to \( 180^\circ \)).
- The diagonals of a rhombus bisect each other at right angles.

2. **Analyzing the Angles**:
- Since \( MNL \) is with respect to the diagonal \( LN \), and we have \( \angle MNL = 55^\circ \), then \( \angle MNO \) (which is adjacent to \( \angle MNL \)) is supplementary to \( \angle MNL \).

3. **Calculate \( m\angle MNO \)**:
- We can set up the equation:
\[
m\angle MNL + m\angle MNO = 180^\circ
\]
- Substituting for \( m\angle MNL \):
\[
55^\circ + m\angle MNO = 180^\circ
\]
- Solving for \( m\angle MNO \):
\[
m\angle MNO = 180^\circ - 55^\circ = 125^\circ
\]

Therefore, the measure of \( m\angle MNO \) is \( 125^\circ \).

### Summary of Steps:
1. Identify the properties of rhombus.
2. Use the fact that \( \angle MNL \) and \( \angle MNO \) are supplementary.
3. Set up the equation and solve for the unknown angle.

Thus, \( m\angle MNO = 125^\circ \).