Chapter 2: Q11 (page 46)

State the number that is paired with the bisector of $∠ C D E$ .

Short Answer

Expert verified

The number paired with bisector of $∠ C D E$ is $70 °$ .

Step by step solution

Step 1. Observe the diagram.

The required number is paired with the bisector of $∠ C D E$ shown in Figure-1 here.

Step 2. State the assumptions and the calculations.

For the calculation, the concept used is the definition of the bisector angle.

Suppose z is the number paired with the bisector of $∠ C D E$ as shown in Figure-2 here,

From Figure-2:

$∠ C D F = 122 °$

$∠ E D F = 18 °$

Assume $∠ B D F = z °$ .

Let $∠ C D B = x °$

That implies

$∠ B D E = x °$ [ since DB is the bisector of $∠ C D E$ ]

Then,

$∠ E D F + ∠ B D E + ∠ C D B = 18 ° + x ° + x °$

Again,

$∠ E D F + ∠ B D E + ∠ C D B = ∠ C D F$

$= 122 °$

Then,

$18 ° + x ° + x ° = 122 °$

$18 ° + 2 x ° = 122 °$

$2 x ° = 104 °$

$x ° = 52 °$

Step 3. State the conclusion.

It is known that $∠ B D F = ∠ B D E + ∠ E D F$ , then,

$∠ B D F = ∠ B D E + ∠ E D F$

$z ° = 18 ° + 52 °$

= 70 °

Therefore, the number paired with the bisector of $∠ C D E$ is $70 °$

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State the number that is paired with the bisector of $∠ C D E$ .

Short Answer

Step by step solution

Step 1. Observe the diagram.

Step 2. State the assumptions and the calculations.

Step 3. State the conclusion.

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State the number that is paired with the bisector of ∠CDE.

Short Answer

Step by step solution

Step 1. Observe the diagram.

Step 2. State the assumptions and the calculations.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Probability and Statistics

Study anywhere. Anytime. Across all devices.

State the number that is paired with the bisector of $∠ C D E$ .