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Use the conditional: If AB¯and CD¯intersect, then ABand CDintersect.

The measure of ABCis 108. BDis the bisector of ABC, and BEis the bisector of ABD. Find the measure of EBC.

Short Answer

Expert verified

The required measurement is 27°.

Step by step solution

01

Step 1. Use the first and second given conditions.

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

ABD=12ABC

02

Step 2. Use the first and third given condition.

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

03

Step 3. Calculate the required measurement.

Using the obtained two equations determine the value of EBC.

EBC=12ABD

=14ABC

=14×108°

=27°

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