Question

parallel lines $overleftrightarrow{ef}$ and $overleftrightarrow{ab}$ are shown with transversal $overleftrightarrow{cd}$ and $mangle adc = 130^{circ}$ and $mangle fcd=8x + 34^{circ}$. what is the value of $x$? $x = square$

Explanation:

Step1: Identify angle - relationship

Since $\overleftrightarrow{EF}\parallel\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ is a transversal, $\angle ADC$ and $\angle FCD$ are same - side interior angles. Same - side interior angles are supplementary, so $m\angle ADC + m\angle FCD=180^{\circ}$.

Step2: Substitute angle measures

We know that $m\angle ADC = 130^{\circ}$ and $m\angle FCD=8x + 34^{\circ}$. Substitute these values into the supplementary - angle equation: $130+(8x + 34)=180$.

Step3: Simplify the equation

First, combine like terms: $130+34+8x=180$, which gives $164+8x=180$.

Step4: Solve for x

Subtract 164 from both sides of the equation: $8x=180 - 164$, so $8x = 16$. Then divide both sides by 8: $x=\frac{16}{8}=2$.

Answer:

$x = 2$