Question

what value of x will show that the top of the third - level of the metalwork, represented by $overline{bd}$, is parallel to the top of the second level, represented by $overline{eg}$? use the drop - down menus to explain your reasoning. $angle bcf$ and $angle efc$ are choose angles. $angle bcf$ and $angle efc$ must be choose for $overline{bd}$ and $overline{eg}$ to be parallel. the equation $(3x - 17)+(2x + 17)=$ choose can be used to determine that x must have a value of choose if the top of the third level is parallel to the top of the second level.

Explanation:

Step1: Identify angle - relationship

If two lines are parallel, then alternate - interior angles are equal. $\angle BCF$ and $\angle EFC$ are alternate - interior angles.

Step2: Set up the equation

Since $\angle BCF=(3x - 17)^{\circ}$ and $\angle EFC=(2x + 17)^{\circ}$, and for $BD\parallel EG$, we set up the equation $3x-17 = 2x + 17$.

Step3: Solve the equation

Subtract $2x$ from both sides: $3x-2x-17=2x - 2x+17$, which gives $x-17 = 17$. Then add 17 to both sides: $x=17 + 17$, so $x = 34$.

Answer:

$x = 34$