Question

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look at this diagram: if (overleftrightarrow{ik}) and (overleftrightarrow{ln}) are parallel lines and (mangle nmj = 113^{circ}), what is (mangle lmo?)

Explanation:

Step1: Identify vertical - angle relationship

$\angle NMJ$ and $\angle IMH$ are vertical angles. Vertical angles are equal. So $m\angle IMH=m\angle NMJ = 113^{\circ}$.

Step2: Identify corresponding - angle relationship

$\overrightarrow{IK}$ and $\overrightarrow{LN}$ are parallel lines. $\angle LMO$ and $\angle IMH$ are corresponding angles. Corresponding angles formed by parallel lines and a transversal are equal.

Answer:

$113$