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: Q19. (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.
$鈭� DHC$

Short Answer

Expert verified

The angle $鈭� D H C$ is $60 掳$ .

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,

$鈭� A H F = 鈭� A H D = 60 掳$ . Since, $\overset{鈫�}{A B}$ bisects $鈭� D H F$ .

$\begin{matrix} 鈭� D H C = 180 鈭� 鈭� A H F 鈭� 鈭� A H D \\ = 180 鈭� 60 鈭� 60 \\ = 60 \end{matrix}$

Hence the angle $鈭� D H C = 60 掳$ .

Step 3. State the conclusion.

Therefore, $鈭� D H C = 60 掳$ .

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Statement	Reason
1. $k 鈭� l$	Given
2. $鈭� 3 鈮� 鈭� 2$	If two parallel lines are cut by transversal then alt. int. $鈭� s$ are $鈮�$
3. $鈭� 1 鈮� 鈭� 3$	Vert. $鈭� s$ are $鈮�$
4. $鈭� 1 鈮� 鈭� 2$	Transitive Property

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.
$鈭� DHC$

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�DHC

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

Applied Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Mechanics Maths

Geometry

Pure Maths

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.
$鈭� DHC$