Question

find the m∠bdg.

Explanation:

Step1: Set up equation

Since the two angles $(4x + 2)^{\circ}$ and $(12x-22)^{\circ}$ are vertical - angles and vertical angles are equal, we set up the equation $4x + 2=12x-22$.

Step2: Solve for x

Subtract $4x$ from both sides: $2 = 12x-4x - 22$, which simplifies to $2=8x - 22$. Then add 22 to both sides: $2 + 22=8x$, so $24 = 8x$. Divide both sides by 8: $x=\frac{24}{8}=3$.

Step3: Find the measure of $\angle BDG$

Substitute $x = 3$ into the expression for $\angle BDG=(4x + 2)^{\circ}$. Then $4x+2=4\times3 + 2=12 + 2=14^{\circ}$.

Answer:

$14^{\circ}$