Question

find the value of (x) and (y). (3x + 17)° (2y + 14)° (6x - 16)°

Explanation:

Step1: Set up equation for x

Since $(3x + 17)^{\circ}$ and $(6x-16)^{\circ}$ are vertical - angles, they are equal. So, $3x + 17=6x - 16$.

Step2: Solve for x

Subtract $3x$ from both sides: $17 = 6x-3x - 16$.
Simplify to get $17 = 3x-16$.
Add 16 to both sides: $17 + 16=3x$, so $33 = 3x$.
Divide both sides by 3: $x=\frac{33}{3}=11$.

Step3: Set up equation for y

Assume the lines are parallel and $(3x + 17)^{\circ}$ and $(2y + 14)^{\circ}$ are corresponding - angles (or other equal - angle relationships depending on the context of parallel lines). Since $x = 11$, then $3x+17=3\times11 + 17=33 + 17 = 50$.
So, $2y+14 = 50$.

Step4: Solve for y

Subtract 14 from both sides: $2y=50 - 14=36$.
Divide both sides by 2: $y=\frac{36}{2}=18$.

Answer:

$x = 11$, $y = 18$