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:
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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.
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Therefore, we can denote:
- m∠MNL = 55 degrees
- m∠NML = 55 degrees
- m∠MNO = x (we need to find this)
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Since ∠MNL and ∠NML form angles at point L along diagonal LN, \[ \text{the angles in triangle MNM: } m∠MNL + m∠NML + m∠MNO = 180^\circ. \]
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Thus, we have: \[ 55 + 55 + m∠MNO = 180, \] \[ 110 + m∠MNO = 180, \] \[ m∠MNO = 180 - 110 = 70 \text{ degrees}. \]
So, m∠MNO = 70 degrees.
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