Question

Rhombus LMNO
has a diagonal line LN¯¯¯¯¯¯¯¯
, and ∠MNL
is 55 degrees. What is m∠MNO
?(1 point)
m∠N=
°

Answer 1

In a rhombus, the diagonals bisect each other at right angles and also bisect the angles of the rhombus.

Given that ∠MNL is 55 degrees, we can determine m∠MNO as follows:

1. Since the diagonals of a rhombus intersect at right angles, we know that ∠MNL and ∠MNO form a linear pair with ∠NMO at point N. Since the diagonals bisect the angles, ∠NML will also be 55 degrees.
2. Therefore, we can denote:
- m∠MNL = 55 degrees
- m∠NML = 55 degrees
- m∠MNO = x (we need to find this)

3. Since ∠MNL and ∠NML form angles at point L along diagonal LN,
\[
\text{the angles in triangle MNM: } m∠MNL + m∠NML + m∠MNO = 180^\circ.
\]
4. Thus, we have:
\[
55 + 55 + m∠MNO = 180,
\]
\[
110 + m∠MNO = 180,
\]
\[
m∠MNO = 180 - 110 = 70 \text{ degrees}.
\]

So, m∠MNO = 70 degrees.