Question

look at this diagram: if (overleftrightarrow{jl}) and (overleftrightarrow{mo}) are parallel lines and (mangle lki = 47^{circ}), what is (mangle lkn)?

Explanation:

Step1: Identify angle - relationship

$\angle LKI$ and $\angle LKN$ are supplementary angles (linear - pair).

Step2: Use supplementary - angle property

The sum of supplementary angles is $180^{\circ}$. So, $m\angle LKI + m\angle LKN=180^{\circ}$.

Step3: Solve for $m\angle LKN$

Given $m\angle LKI = 47^{\circ}$, then $m\angle LKN=180^{\circ}-m\angle LKI$. Substitute $m\angle LKI = 47^{\circ}$ into the equation: $m\angle LKN = 180 - 47=133^{\circ}$.

Answer:

$133$