Question

9/22 -angles mixed practice given the picture and bd bisects ∠abc. set up and equation to solve for x and find x. equation (type in with no spaces): x=

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{BD}$ bisects $\angle ABC$, then $\angle ABD=\angle DBC$. So, we set up the equation $2x + 7=4x-9$.

Step2: Solve the equation for $x$

First, subtract $2x$ from both sides: $2x+7 - 2x=4x - 9-2x$, which simplifies to $7 = 2x-9$.
Then, add 9 to both sides: $7 + 9=2x-9 + 9$, getting $16 = 2x$.
Finally, divide both sides by 2: $\frac{16}{2}=\frac{2x}{2}$, so $x = 8$.

Answer:

Equation: $2x + 7=4x-9$
$x = 8$