Question

3.4.6 check your understanding
in the figure shown, $overline{nd}paralleloverline{hp}$, and $overline{rt}$ and $overline{sb}$ are transversals with $mangle rgw = 142^{circ}$ and $mangle bml=121^{circ}$.
determine the measurement of the angles.
m$angle tlp =$
m$angle dws =$
m$angle hmb =$
m$angle gkw =$

$38^{circ}$ # $59^{circ}$ # $47^{circ}$ # $83^{circ}$

Explanation:

Step1: Identify corresponding - angle relationship for $\angle TLP$

$\angle RGW$ and $\angle TLP$ are corresponding angles. Since $\overline{ND}\parallel\overline{HP}$, $m\angle TLP = m\angle RGW$. Given $m\angle RGW = 142^{\circ}$, so $m\angle TLP=142^{\circ}$.

Step2: Identify vertical - angle relationship for $\angle DWS$

$\angle DWS$ and $\angle GKW$ are vertical angles. First, find $\angle GKW$. $\angle RGW$ and $\angle GKW$ are supplementary (linear - pair). So $m\angle GKW=180^{\circ}-m\angle RGW = 180 - 142=38^{\circ}$. Since vertical angles are equal, $m\angle DWS = 38^{\circ}$.

Step3: Identify vertical - angle relationship for $\angle HMB$

$\angle HMB$ and $\angle BML$ are supplementary (linear - pair). Given $m\angle BML = 121^{\circ}$, then $m\angle HMB=180^{\circ}-m\angle BML=180 - 121 = 59^{\circ}$.

Step4: We already found $\angle GKW$ in Step 2

As calculated before, $m\angle GKW = 38^{\circ}$.

Answer:

$m\angle TLP = 142^{\circ}$
$m\angle DWS = 38^{\circ}$
$m\angle HMB = 59^{\circ}$
$m\angle GKW = 38^{\circ}$