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 $m\mathrm{\angle }MNO$ 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 $m\mathrm{\angle }MNL={55}^{\circ }$.

3. Using the Angles: In rhombus $LMNO$:

   • Since the diagonals bisect the angles, we know that: $$m\mathrm{\angle }MNL=m\mathrm{\angle }NLM$$ Hence: $$m\mathrm{\angle }NLM={55}^{\circ }$$

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 ${180}^{\circ }$): $$m\mathrm{\angle }MNO+m\mathrm{\angle }NLM={180}^{\circ }$$ Substituting known values: $$m\mathrm{\angle }MNO+{55}^{\circ }={180}^{\circ }$$

5. Solving for $m\mathrm{\angle }MNO$: $$m\mathrm{\angle }MNO={180}^{\circ }-{55}^{\circ }={125}^{\circ }$$

Thus, the measure of angle $m\mathrm{\angle }MNO$ is ${125}^{\circ }$.

Final Answer: $$m\mathrm{\angle }MNO={125}^{\circ }$$