Question

in the diagram above, (mangle abe=(5x + 1)^{circ}), (overline{eb}) is the bisector of (mangle abc), and (mangle dbf = 90^{circ}). find the value of (x). answer

Explanation:

Step1: Identify vertical - angles

Vertical angles are equal. $\angle ABE$ and $\angle DBF$ are vertical angles. Since $\angle DBF = 90^{\circ}$, then $\angle ABE=90^{\circ}$.

Step2: Set up the equation

We know that $m\angle ABE=(5x + 1)^{\circ}$ and $m\angle ABE = 90^{\circ}$. So we set up the equation $5x+1 = 90$.

Step3: Solve the equation for $x$

Subtract 1 from both sides: $5x=90 - 1$, so $5x=89$. Then divide both sides by 5: $x=\frac{89}{5}=17.8$.

Answer:

$17.8$