Question

in the figure, $overleftrightarrow{hl}paralleloverleftrightarrow{yr}$, $overleftrightarrow{nb}paralleloverleftrightarrow{gw}$, $angle fbx$ is a right - angle, and $mangle xwb = 37^{circ}$. select all of the equations that must be true. $square mangle bfx = 37^{circ}$ $square mangle bxf = 37^{circ}$ $square mangle lxw = 143^{circ}$ $square mangle wbx = 37^{circ}$ $square mangle wxl = 37^{circ}$ $square mangle ybm = 143^{circ}$

Explanation:

Step1: Identify corresponding - angles

Since $NB\parallel GW$ and $\angle XWB = 37^{\circ}$, $\angle BFX$ and $\angle XWB$ are corresponding - angles. So, $m\angle BFX=37^{\circ}$.

Step2: Identify supplementary - angles

$\angle LXW$ and $\angle XWB$ are supplementary angles (linear pair). Since $\angle XWB = 37^{\circ}$, then $m\angle LXW=180 - 37=143^{\circ}$.

Step3: Identify vertical - angles

$\angle YBM$ and $\angle LXW$ are vertical angles. Since $m\angle LXW = 143^{\circ}$, then $m\angle YBM = 143^{\circ}$.

Answer:

$m\angle BFX = 37^{\circ}$, $m\angle LXW = 143^{\circ}$, $m\angle YBM = 143^{\circ}$