Question

1. in the figure $overleftrightarrow{ef}$ and $overleftrightarrow{hg}$ are parallel. solve for $x$ if $mangle abf = 125^{circ}$ and $mangle hcd=3x + 5$.

Explanation:

Step1: Identify angle - relationship

Since $\overline{EF}$ and $\overline{HG}$ are parallel, $\angle HCD$ and $\angle ABF$ are corresponding angles and are congruent. So $m\angle HCD=m\angle ABF$.

Step2: Set up the equation

We know that $m\angle HCD = 3x + 5$ and $m\angle ABF=125^{\circ}$, so we set up the equation $3x + 5=125$.

Step3: Solve the equation for x

Subtract 5 from both sides: $3x=125 - 5=120$. Then divide both sides by 3: $x=\frac{120}{3}=40$.

Answer:

$40$