Question

1. in the diagram, $overleftrightarrow{de}paralleloverleftrightarrow{fh}$. find the measure of $angle jge$.

Explanation:

Step1: Use corresponding - angles property

Since $\overrightarrow{DE}\parallel\overrightarrow{FH}$, the angles $(\frac{2}{3}t + 5)^{\circ}$ and $(\frac{1}{2}t+\frac{35}{2})^{\circ}$ are corresponding angles and are equal. So we set up the equation $\frac{2}{3}t + 5=\frac{1}{2}t+\frac{35}{2}$.

Step2: Solve the equation for $t$

First, get a common - denominator for the $t$ terms. Multiply through by 6 to clear the fractions: $6\times(\frac{2}{3}t)+6\times5 = 6\times(\frac{1}{2}t)+6\times\frac{35}{2}$.
This simplifies to $4t + 30=3t + 105$.
Subtract $3t$ from both sides: $4t-3t+30=3t - 3t+105$, which gives $t + 30=105$.
Then subtract 30 from both sides: $t=105 - 30=75$.

Step3: Find the measure of $\angle{JGE}$

Substitute $t = 75$ into the expression for $\angle{JGE}$, which is $\frac{2}{3}t+5$.
$\frac{2}{3}\times75 + 5=50 + 5=55^{\circ}$.

Answer:

$55^{\circ}$