Rhombus Proofs Practice

Question

Complete this assessment to review what you’ve learned. It will not count toward your grade.
3 of 53 of 5 Items

Question
Rhombus LMNO
has a diagonal line LN¯¯¯¯¯¯¯¯
, and ∠MNL
is 55 degrees. What is m∠MNO
?(1 point)
m∠N=
°
Remaining Attempts : 2View previous attempt

Answer 1

To solve for \( m\angle MNO \) in rhombus \( LMNO \):

1. Properties of Rhombus: In a rhombus, the diagonals bisect each other at right angles and the opposite angles are equal.

2. Given Information: You are given that \( m\angle MNL = 55^\circ \).

3. Using the Angles: In rhombus \( LMNO \):

   • Since the diagonals bisect the angles, we know that: \[ m\angle MNL = m\angle NLM \] Hence: \[ m\angle NLM = 55^\circ \]

4. Finding Angles in a Rhombus: The measure of opposite angles in a rhombus are equal, and adjacent angles are supplementary (they add up to \( 180^\circ \)): \[ m\angle MNO + m\angle NLM = 180^\circ \] Substituting known values: \[ m\angle MNO + 55^\circ = 180^\circ \]

5. Solving for \( m\angle MNO \): \[ m\angle MNO = 180^\circ - 55^\circ = 125^\circ \]

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

Final Answer: \[ m\angle MNO = 125^\circ \]