Chapter 2: Q7 (page 49)

Use the conditional: If $\bar{A B}$ and $\bar{C D}$ intersect, then $\vec{A B}$ and $\vec{C D}$ intersect.
The measure of $∠ A B C$ is 108. $\vec{B D}$ is the bisector of $∠ A B C$ , and $\vec{B E}$ is the bisector of $∠ A B D$ . Find the measure of $∠ E B C$ .

Short Answer

Expert verified

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 $∠ A B C$ so make an equation for this with the help of angle bisector theorem.

$∠ A B D = \frac{1}{2} ∠ A B C$

Step 2. Use the first and third given condition.

As the ray BE represents itself as the bisections that is for $∠ A B D$ 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 $∠ E B C$ .

$∠ E B C = \frac{1}{2} ∠ A B D$

$= \frac{1}{4} ∠ A B C$

$= \frac{1}{4} \times 108 °$

$= 27 °$

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Use the conditional: If $\bar{A B}$ and $\bar{C D}$ intersect, then $\vec{A B}$ and $\vec{C D}$ intersect.
The measure of $∠ A B C$ is 108. $\vec{B D}$ is the bisector of $∠ A B C$ , and $\vec{B E}$ is the bisector of $∠ A B D$ . Find the measure of $∠ E B C$ .

Short Answer

Step by step solution

Step 1. Use the first and second given conditions.

Step 2. Use the first and third given condition.

Step 3. Calculate the required measurement.

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Use the conditional: If AB¯and CD¯intersect, then AB→and CD→intersect.The measure of ∠ABCis 108. BD→is the bisector of ∠ABC, and BE→is the bisector of ∠ABD. Find the measure of ∠EBC.

Short Answer

Step by step solution

Step 1. Use the first and second given conditions.

Step 2. Use the first and third given condition.

Step 3. Calculate the required measurement.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Geometry

Theoretical and Mathematical Physics

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Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Use the conditional: If $\bar{A B}$ and $\bar{C D}$ intersect, then $\vec{A B}$ and $\vec{C D}$ intersect.
The measure of $∠ A B C$ is 108. $\vec{B D}$ is the bisector of $∠ A B C$ , and $\vec{B E}$ is the bisector of $∠ A B D$ . Find the measure of $∠ E B C$ .