Chapter 4: Q3. (page 165)

Complete each sentence with the most appropriate word, phase or value.
$\overset{\leftrightarrow}{BD}$ bisects $∠ ABC$ , $m ∠ ABC = 5 x - 4$ and $m ∠ CBD = 2 x + 10$ . $∠ ABC$ is a(n) ________ angle.

Short Answer

Expert verified

The answer is Obtuse Angle.

Step by step solution

Step 1. State the property of bisector.

There are two properties of a bisector:

1. Any point on the bisector of an angle is equidistant from the sides of the angle.

2. In a triangle, the angle bisector divides the opposite side in the ratio of the adjacent sides.

Step 2. State the explanation.

By using the property of the bisector,

$\begin{matrix} m ∠ A B C = 2 m ∠ C B D \\ 5 x - 4 = 2 (2 x + 10) \\ 5 x - 4 = 4 x + 20 \\ 5 x - 4 x = 20 + 4 \\ x = 24 \end{matrix}$

Then,

$\begin{matrix} m ∠ A B C = 5 (24) - 4 \\ = 116 \end{matrix}$

Since the measure of the angle is greater than 90 degrees but less than 180 degrees, $m ∠ A B C$ is an obtuse angle.

Hence, the blank is filled by the term “Obtuse Angle”.

Step 3. State the conclusion.

Therefore, “ $\vec{B D}$ bisects $∠ A B C$ , $m ∠ A B C = 5 x - 4$ and $m ∠ C B D = 2 x + 10$ . $∠ A B C$ is a(n) obtuse angle”.

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Complete each sentence with the most appropriate word, phase or value.
$\overset{\leftrightarrow}{BD}$ bisects $∠ ABC$ , $m ∠ ABC = 5 x - 4$ and $m ∠ CBD = 2 x + 10$ . $∠ ABC$ is a(n) ________ angle.

Short Answer

Step by step solution

Step 1. State the property of bisector.

Step 2. State the explanation.

Step 3. State the conclusion.

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Complete each sentence with the most appropriate word, phase or value.BD↔bisects ∠ABC,m∠ABC=5x−4and m∠CBD=2x+10. ∠ABCis a(n) ________ angle.

Short Answer

Step by step solution

Step 1. State the property of bisector.

Step 2. State the explanation.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Theoretical and Mathematical Physics

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Decision Maths

Study anywhere. Anytime. Across all devices.

Complete each sentence with the most appropriate word, phase or value.
$\overset{\leftrightarrow}{BD}$ bisects $∠ ABC$ , $m ∠ ABC = 5 x - 4$ and $m ∠ CBD = 2 x + 10$ . $∠ ABC$ is a(n) ________ angle.