Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 3: Q20. (page 114)

In the diagram $\overset{鈫�}{AB}$ bisects $鈭� DHF$ , $\overset{鈫�}{AB} 鈯� \overset{炉}{GH}$ , $\overset{鈫�}{AB} 鈭� \overset{鈫�}{CD}$ , and $m 鈭� AHB= 60 掳$ . Find the measure of each angle.
$鈭� H D E$ .

Short Answer

Expert verified

The angle $鈭� H D E$ is $120 掳$ .

Step by step solution

Step 1. Observe the diagram.

Here, $鈭� A H D = 60 掳$ , $\overset{鈫�}{A B} 鈯� \overset{炉}{G H}$ , $\overset{鈫�}{A B} 鈭� \overset{鈫�}{C D}$ and $\overset{鈫�}{A B}$ bisects $鈭� D H F$ .

Step 2. Show the calculation.

From the figure and the data,

As, $\overset{鈫�}{A B} 鈭� \overset{鈫�}{C D}$ , $\overset{鈫�}{A B} 鈭� \overset{鈫�}{C E}$ .

(As $\overset{鈫�}{C E}$ is the extended part of $\overset{鈫�}{C D}$ )

Take $\overset{鈫�}{H D}$ as a transversal.

Use the fact that if a transversal intersects two parallel lines, then sum of each pair of co-interior angles is $180 掳$ .

So,

$鈭� A H D + 鈭� H D E = 180 掳$

Put $鈭� A H D = 60 掳$ .

Then,

$\begin{matrix} 60^{鈭�} + 鈭� H D E = 180^{鈭�} \\ 鈭� H D E = 180^{鈭�} 鈭� 60^{鈭�} \\ = 120^{鈭�} \end{matrix}$

Hence the angle $鈭� H D E = 120 掳$ .

Step 3. State the conclusion.

Therefore, $鈭� H D E = 120 掳$ .

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91影视

In the diagram $\overset{鈫�}{AB}$ bisects $鈭� DHF$ , $\overset{鈫�}{AB} 鈯� \overset{炉}{GH}$ , $\overset{鈫�}{AB} 鈭� \overset{鈫�}{CD}$ , and $m 鈭� AHB= 60 掳$ . Find the measure of each angle.
$鈭� H D E$ .

Short Answer

Step by step solution

Step 1. Observe the diagram.

Step 2. Show the calculation.

Step 3. State the conclusion.

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91影视

In the diagram AB鈫�bisects 鈭�DHF, AB鈫�鈯�GH炉, AB鈫�鈭�CD鈫�, and m鈭�AHB=60掳. Find the measure of each angle.鈭�HDE.

Short Answer

Step by step solution

Step 1. Observe the diagram.

Step 2. Show the calculation.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Statistics

Calculus

Discrete Mathematics

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the diagram $\overset{鈫�}{AB}$ bisects $鈭� DHF$ , $\overset{鈫�}{AB} 鈯� \overset{炉}{GH}$ , $\overset{鈫�}{AB} 鈭� \overset{鈫�}{CD}$ , and $m 鈭� AHB= 60 掳$ . Find the measure of each angle.
$鈭� H D E$ .