Question

given $m\angle rhw=(x + 20)^{circ}$ and $m\angle mgf=(9x + 5)^{circ}$. complete the statement. the $m\angle wht$ is because it is congruent to

Explanation:

Step1: Identify angle - relationships

Since $\overrightarrow{ML}\parallel\overrightarrow{RT}$ and $\overrightarrow{FW}$ is a transversal, $\angle RHW$ and $\angle MGF$ are corresponding angles. So, $\angle RHW=\angle MGF$.

Step2: Set up the equation

We have the equation $x + 20=9x+5$.

Step3: Solve the equation for $x$

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

Step4: Find $\angle RHW$

Substitute $x = \frac{15}{8}$ into the expression for $\angle RHW$: $m\angle RHW=\frac{15}{8}+20=\frac{15 + 160}{8}=\frac{175}{8}=21.875^{\circ}$.

Step5: Use vertical - angle property

$\angle WHT$ and $\angle RHW$ are vertical angles. Vertical angles are congruent. So $m\angle WHT=m\angle RHW$.

Answer:

The $m\angle WHT$ is $(x + 20)^{\circ}$ (or $21.875^{\circ}$ when $x=\frac{15}{8}$) because it is congruent to $\angle RHW$.