Question

parallel $overleftrightarrow{ab}$ and $overleftrightarrow{cd}$ are shown with transversal $overleftrightarrow{ef}$. $mangle ahf = 60^{circ}$ and $mangle dke=(8x + 4)^{circ}$. solve for x. x =

Explanation:

Step1: Identify angle - relationship

Since $\overleftrightarrow{AB}\parallel\overleftrightarrow{CD}$ and $\overleftrightarrow{EF}$ is a transversal, $\angle AHF$ and $\angle DKE$ are corresponding angles. Corresponding angles are congruent when two parallel lines are cut by a transversal. So, $m\angle AHF=m\angle DKE$.

Step2: Set up the equation

We know that $m\angle AHF = 60^{\circ}$ and $m\angle DKE=(8x + 4)^{\circ}$. Set up the equation $8x+4 = 60$.

Step3: Solve the equation for x

Subtract 4 from both sides of the equation: $8x=60 - 4$, so $8x=56$. Then divide both sides by 8: $x=\frac{56}{8}=7$.

Answer:

$7$