Question

in the diagram above, (mangle abe=(5x + 1)^{circ}), (overline{eb}) is the bisector of (mangle abc), and (mangle dbf = 82^{circ}). find the value of (x).

Explanation:

Step1: Identify vertical - angles

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

Step2: Set up the equation

Since $m\angle ABE=(5x + 1)^{\circ}$ and $m\angle DBF = 82^{\circ}$, we have the equation $5x+1 = 82$.

Step3: Solve the equation for $x$

Subtract 1 from both sides: $5x=82 - 1=81$. Then divide both sides by 5: $x=\frac{81}{5}=16.2$.

Answer:

$16.2$