Question

given the figure below, find the values of x and z.

Explanation:

Step1: Use vertical - angles property

Vertical angles are equal. So, $14x - 68=6x + 8$.

Step2: Solve for x

Subtract $6x$ from both sides: $14x-6x - 68=6x-6x + 8$, which simplifies to $8x-68 = 8$. Then add 68 to both sides: $8x-68 + 68=8 + 68$, giving $8x=76$. Divide both sides by 8: $x=\frac{76}{8}=\frac{19}{2}=9.5$.

Step3: Find the value of z

We know that $z$ and $(6x + 8)$ are supplementary (a linear - pair, so their sum is 180°). First, find the value of $6x + 8$ when $x = 9.5$. $6x+8=6\times9.5 + 8=57 + 8=65$. Then, since $z+(6x + 8)=180$, $z=180-(6x + 8)=180 - 65 = 115$.

Answer:

$x = 9.5$, $z = 115$