Question
Rhombus LMNO has a diagonal line MO¯¯¯¯¯¯¯¯¯ , with m∠M=74° . What is m∠LOM ?
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Answered by
GPT-4o mini
In a rhombus, the diagonals bisect each other at right angles and also bisect the angles of the rhombus. Given that \( m\angle M = 74^\circ \), we can determine the other angles using the properties of a rhombus.
1. Since the diagonals bisect the angles, we know that \( m\angle LOM \) will be half of \( m\angle M \). Therefore, we can calculate \( m\angle LOM \):
\[
m\angle LOM = \frac{1}{2} m\angle M = \frac{1}{2} \cdot 74^\circ = 37^\circ
\]
Thus, \( m\angle LOM = 37^\circ \).
1. Since the diagonals bisect the angles, we know that \( m\angle LOM \) will be half of \( m\angle M \). Therefore, we can calculate \( m\angle LOM \):
\[
m\angle LOM = \frac{1}{2} m\angle M = \frac{1}{2} \cdot 74^\circ = 37^\circ
\]
Thus, \( m\angle LOM = 37^\circ \).
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