Question

Rhombus LMNO
has a diagonal line LN¯¯¯¯¯¯¯¯
, and ∠MNL
is 55 degrees. What is m∠MNO
?(1 point)
m∠N=
° which answer is correct how do you solve it and why

Answer 1

In a rhombus, the properties of its angles and diagonals can help us find the measure of the angles.

1. In a rhombus, the diagonals bisect each other at right angles.
2. The diagonals divide the rhombus into four triangles.
3. The diagonals also bisect the angles of the rhombus.

Given:
- \( \angle MNL = 55^\circ \)
- The diagonal \( LN \) divides \( \angle MNL \) into two equal angles, because the diagonals bisect the angles.

Since \( LN \) bisects \( \angle MNL \):
\[ \angle MNL = \angle MNO + \angle NML \]

Let's denote:
- \( \angle MNL = 55^\circ \)
- \( \angle NML = 55^\circ \) (because opposite angles are equal in a rhombus and \( \angle NML \) is equal to \( \angle MNL \))

The angles around point \( N \) in triangle \( MNL \):
Since \( LN \) is a diagonal, it also implies that:
\[ m\angle MNO + m\angle MNL + m\angle LNM = 180^\circ \]

Since \( \angle MNL = 55^\circ \) and \( \angle LNM = \angle MNL = 55^\circ \):
Thus:
\[ m\angle MNO + 55^\circ + 55^\circ = 180^\circ \]

Now solving for \( m\angle MNO \):
\[ m\angle MNO + 110^\circ = 180^\circ \]
\[ m\angle MNO = 180^\circ - 110^\circ \]
\[ m\angle MNO = 70^\circ \]

Thus, the measure of angle \( MNO \) is \( 70^\circ \).

So, the final answer is:
\[ m\angle MNO = 70^\circ \]