Question

look at this diagram:
if (overleftrightarrow{ik}) and (overleftrightarrow{ln}) are parallel lines and (mangle lmj = 47^{circ}), what is (mangle kjh)?
(square^{circ})

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. $\angle LMJ$ and $\angle IJM$ are vertical angles. So, $m\angle IJM = m\angle LMJ=47^{\circ}$.

Step2: Use the property of parallel lines and transversal

Since $\overleftrightarrow{IK}$ and $\overleftrightarrow{LN}$ are parallel and $OH$ is a transversal, $\angle IJM$ and $\angle KJH$ are supplementary (they form a linear - pair). But wait, no, actually, if we consider the straight - line property. Wait, no, another approach: $\angle LMJ$ and $\angle KJH$ are corresponding angles. Wait, no, correct approach: $\angle LMJ$ and $\angle IJM$ are vertical angles ($\angle LMJ=\angle IJM = 47^{\circ}$). And $\angle IJM$ and $\angle KJH$ are supplementary (they form a linear pair: $\angle IJM+\angle KJH = 180^{\circ}$). Wait, no, wrong. Wait, correct: $\angle LMJ$ and $\angle KJH$ are supplementary. Wait, no, correct: $\angle LMJ$ and $\angle IJM$ are vertical angles ($m\angle IJM = 47^{\circ}$). Since $\overleftrightarrow{IK}\parallel\overleftrightarrow{LN}$, and $OH$ is a transversal, $\angle IJM$ and $\angle KJH$ are supplementary (same - side interior angles). Wait, no, wrong. Correct: $\angle LMJ$ and $\angle KJH$ are supplementary. Wait, no, correct: $\angle LMJ$ and $\angle IJM$ are vertical angles ($m\angle IJM=47^{\circ}$). $\angle IJM$ and $\angle KJH$ are on a straight line (linear pair). Wait, no, $\angle LMJ$ and $\angle KJH$: Since $\overleftrightarrow{IK}\parallel\overleftrightarrow{LN}$, and $OH$ is a transversal, $\angle LMJ$ and $\angle KJH$ are supplementary (same - side interior angles). Wait, no, $\angle LMJ$ and $\angle IJM$ are vertical angles ($\angle IJM = 47^{\circ}$). $\angle IJM$ and $\angle KJH$: $\angle IJM+\angle KJH=180^{\circ}$ (linear pair). So $m\angle KJH=180 - 47=133^{\circ}$.

Answer:

$133$