Question

1. $overleftrightarrow{rw}paralleloverleftrightarrow{xh}$, $mangle ryk = s^{circ}$, $mangle cyw = m^{circ}$, $mangle gyb = 43^{circ}$, $mangle ybg = 72^{circ}$, and $mangle lgh=(6t + 11)^{circ}$. find the value of each variable. show your work. $t$

Explanation:

Step1: Identify vertical - angles

$\angle GYB$ and $\angle CY W$ are vertical - angles. So, $m\angle CY W=m\angle GYB = 43^{\circ}$, then $m = 43$.

Step2: Use the property of adjacent angles on a straight - line

$\angle YBG$ and $\angle YBH$ form a linear pair. So, $m\angle YBH=180^{\circ}-m\angle YBG=180 - 72=108^{\circ}$.

Step3: Use the property of corresponding angles for parallel lines

Since $\overline{RW}\parallel\overline{XH}$, $\angle LGH$ and $\angle YBH$ are corresponding angles. So, $m\angle LGH=m\angle YBH$.
Set up the equation: $6t + 11=108$.

Step4: Solve the equation for $t$

Subtract 11 from both sides of the equation: $6t=108 - 11=97$.
Divide both sides by 6: $t=\frac{97}{6}\approx16.17$.

Answer:

$t=\frac{97}{6}$