Question

Use the conditional: If $\overline{AB}$and $\overline{CD}$intersect, then $\overrightarrow{AB}$and $\overrightarrow{CD}$intersect.

The measure of $\angle ABC$is 108. $\overrightarrow{BD}$is the bisector of $\angle ABC$, and $\overrightarrow{BE}$is the bisector of $\angle ABD$. Find the measure of $\angle EBC$.

Short answer

The required measurement is $27°$.

Step-by-step solution

Step 1. Use the first and second given conditions.

As the ray BD represents itself as the bisections that is for $\angle ABC$so make an equation for this with the help of angle bisector theorem.

$\angle ABD=\frac{1}{2}\angle ABC$

Step 2. Use the first and third given condition.

As the ray BE represents itself as the bisections that is for$\angle ABD$ so make an equation for this with the help of angle bisector theorem.

Step 3. Calculate the required measurement.

Using the obtained two equations determine the value of $\angle EBC$.

$\angle EBC=\frac{1}{2}\angle ABD$

$=\frac{1}{4}\angle ABC$

$=\frac{1}{4}\times 108°$

$=27°$