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Chapter 2: Q7 (page 49)

Use the conditional: If AB炉and CD炉intersect, then AB鈫�and CD鈫�intersect.

The measure of 鈭�ABCis 108. BD鈫�is the bisector of 鈭�ABC, and BE鈫�is the bisector of 鈭�ABD. Find the measure of 鈭�EBC.

Short Answer

Expert verified

The required measurement is 27掳.

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 鈭�ABCso make an equation for this with the help of angle bisector theorem.

鈭�ABD=12鈭�ABC

02

Step 2. Use the first and third given condition.

As the ray BE represents itself as the bisections that is for鈭�ABD 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 鈭�EBC.

鈭�EBC=12鈭�ABD

=14鈭�ABC

=14脳108掳

=27掳

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Most popular questions from this chapter

Write a definition of congruent angles as a biconditional.

Copy everything shown and supply missing statements and reasons.

Given: 鈭�AODas shown

Prove: m鈭�AOD=m鈭�1+m鈭�2+m鈭�3

Proof:

State the number that is paired with the bisector of 鈭�CDE.

State which definition, postulate, or theorem justifies the statement about the diagram.

m鈭�3+m鈭�4=180

Provide a counterexample to show that each statement is false.

Statement: If a four-sided figure has four right angles, then it has four congruent sides.
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