Q5. In the diagram above聽r鈭.If聽... [FREE SOLUTION]

91影视

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: Q5. (page 111)

In the diagram above $r 鈭� s$ .
Ifrole="math" localid="1650004659239" $m 鈭� 1 = 105$ then $m 鈭� 5 = ?$ and $m 鈭� 7 = ?$

Short Answer

Expert verified

The measure of $鈭� 5$ and $鈭� 7$ are 105 and 105 respectively.

Step by step solution

Step 1. Highlight ∠5, ∠1 and ∠7 in the given diagram.

Step 2. Apply the property of parallel lines.

If the two parallel lines are intersected by a transversal, then the corresponding angles are congruent.

Step 3. Description of step.

From the given figure it can be observed that $r 鈭� s$ and $t$ is transversal then by the definition of corresponding angles, $鈭� 5$ and $鈭� 1$ are corresponding angles.

Therefore, $鈭� 1 鈮� 鈭� 5$ , that is, $m 鈭� 5 = m 鈭� 1 = 105$ .

Step 4. Description of step.

From the given figure it can be observed that and is transversal then by the properties of parallel lines, $鈭� 1$ and $鈭� 7$ are alternate exterior angles.

Therefore, $m 鈭� 7 = m 鈭� 1 = 105$ .

Therefore, the measures of $鈭� 5$ and $鈭� 7$ are 105 and 105 respectively.

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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 above $r 鈭� s$ .
Ifrole="math" localid="1650004659239" $m 鈭� 1 = 105$ then $m 鈭� 5 = ?$ and $m 鈭� 7 = ?$

Short Answer

Step by step solution

Step 1. Highlight ∠5, ∠1 and ∠7 in the given diagram.

Step 2. Apply the property of parallel lines.

Step 3. Description of step.

Step 4. Description of step.

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91影视

In the diagram abover鈭�s.Ifrole="math" localid="1650004659239" m鈭�1=105 thenm鈭�5=?andm鈭�7=?

Short Answer

Step by step solution

Step 1. Highlight ∠5, ∠1 and ∠7 in the given diagram.

Step 2. Apply the property of parallel lines.

Step 3. Description of step.

Step 4. Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Geometry

Theoretical and Mathematical Physics

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the diagram above $r 鈭� s$ .
Ifrole="math" localid="1650004659239" $m 鈭� 1 = 105$ then $m 鈭� 5 = ?$ and $m 鈭� 7 = ?$