Question

look at this diagram: if (overrightarrow{jl}) and (overrightarrow{mo}) are parallel lines and (mangle onk = 65^{circ}), what is (mangle lkn?)

Explanation:

Step1: Identify angle - type relationship

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

Step2: Use the supplementary - angle property

The sum of two supplementary angles is $180^{\circ}$. Let $m\angle ONK = 65^{\circ}$ and $m\angle LKN=x$. Then $m\angle ONK + m\angle LKN=180^{\circ}$, so $x = 180^{\circ}-m\angle ONK$.

Step3: Calculate the angle measure

Substitute $m\angle ONK = 65^{\circ}$ into the equation: $x=180 - 65=115^{\circ}$.

Answer:

$115$