Question

consider the following diagram. in the diagram above, (mangle abe=(5x + 1)^{circ}), (overline{eb}) is the bisector of (mangle abc), and (mangle dbf = 83^{circ}). find the value of (x).

Explanation:

Step1: Identify vertical - angles

Vertical angles are equal. $\angle ABE$ and $\angle DBF$ are vertical angles. So, $m\angle ABE=m\angle DBF$.

Step2: Set up the equation

Since $m\angle ABE=(5x + 1)^{\circ}$ and $m\angle DBF = 83^{\circ}$, we set up the equation $5x+1 = 83$.

Step3: Solve for x

Subtract 1 from both sides of the equation: $5x=83 - 1$, so $5x=82$. Then divide both sides by 5: $x=\frac{82}{5}=16.4$.

Answer:

$x = 16.4$