Question

ml || rt, where fw is a transversal. given m∠rhw=(x + 20)° and m∠mgf=(9x + 5)°. the m∠wht is 144.5° because it is congruent to ∠mgf.

Explanation:

Step1: Use corresponding - angles property

Since $\overrightarrow{ML}\parallel\overrightarrow{RT}$ and $\overrightarrow{FW}$ is a transversal, $\angle RHW$ and $\angle MGF$ are corresponding - angles, so $\angle RHW=\angle MGF$.
$(x + 20)=(9x+5)$.

Step2: Solve the equation for $x$

Subtract $x$ from both sides: $20 = 8x+5$.
Subtract 5 from both sides: $15 = 8x$.
Then $x=\frac{15}{8}=1.875$.

Step3: Find the measure of $\angle MGF$

Substitute $x = 1.875$ into the expression for $\angle MGF$: $m\angle MGF=(9x + 5)^{\circ}=(9\times1.875+5)^{\circ}=(16.875 + 5)^{\circ}=21.875^{\circ}$. This is wrong. Let's use the property of vertical - angles and corresponding - angles correctly.
Since $\overrightarrow{ML}\parallel\overrightarrow{RT}$ and $\overrightarrow{FW}$ is a transversal, $\angle RHW$ and $\angle MGF$ are corresponding angles, so $\angle RHW=\angle MGF$.
We know that $\angle WHT$ and $\angle RHW$ are supplementary (linear - pair of angles), and $\angle WHT$ and $\angle MGF$ are corresponding angles.
Since $\angle RHW$ and $\angle MGF$ are corresponding angles, $x + 20=9x+5$.
$8x=15$, $x=\frac{15}{8}$.
$\angle RHW=x + 20=\frac{15}{8}+20=\frac{15 + 160}{8}=\frac{175}{8}=21.875^{\circ}$.
$\angle WHT = 180^{\circ}-\angle RHW$.
$m\angle WHT=180-(x + 20)$.
Since $\angle WHT=\angle MGF$ (corresponding angles for parallel lines), we have:
$180-(x + 20)=9x+5$.
$180 - x-20=9x+5$.
$160 - x=9x+5$.
$10x=155$.
$x = 15.5$.
$m\angle MGF=9x+5=9\times15.5+5=139.5 + 5=144.5^{\circ}$.
$\angle WHT$ and $\angle MGF$ are corresponding angles for parallel lines $\overrightarrow{ML}$ and $\overrightarrow{RT}$ with transversal $\overrightarrow{FW}$, so $\angle WHT=\angle MGF$.

Answer:

$144.5^{\circ}$