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K Step 3: Two parallel lines cut by a transversal For our safety, it is important that drivers recognize a stop sign immediately. Stop signs are made with exact side and angle measurements to form a regular octagon. They are red so they are easy to see. The three lines drawn below are straight lines. Lines a and b are parallel. a b C HE G F STOP K J

K Step 3: Two parallel lines cut by a transversal For our safety, it is important that drivers recognize a stop sign immediately. Stop signs are made with exact side and angle measurements to form a regular octagon. They are red so they are easy to see. The three lines drawn below are straight lines. Lines a and b are parallel. a b C HE G F STOP K J

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Step 3: Two parallel lines cut by a transversal** For our safety, it is important that drivers recognize a stop sign immediately. Stop signs are made with exact side and angle measurements to form a regular octagon. They are red so they are easy to see. The three lines drawn below are straight lines. Lines **a** and **b** are parallel. ### Diagram Explanation: The diagram features two parallel lines labeled **a** and **b**, with a red octagonal stop sign placed between them. These lines are intersected by a transversal line labeled **c**. Several points are marked at the intersections: - Point **H** is where the transversal **c** intersects the upper parallel line **a**. - Point **G** is directly where line **a** intersects the edge of the stop sign. - Point **F** is above the stop sign where the letter 'O' appears. - Point **E** is toward the top just above where the transversal **c** starts. - Point **L** is where the transversal **c** intersects the lower parallel line **b**. - Points **I** and **J** are at the intersections where line **b** crosses just below the stop sign. - Point **K** is along the line **c** between points **L** and **J**. The arrows at the end of the parallel lines **a** and **b** indicate that they extend infinitely in the directions shown. This diagram visually reinforces the concept of parallel lines being consistently the same distance apart and intersected by a transversal, creating specific angle relationships, which help drivers recognize traffic signs efficiently.
Transcribed Image Text:**Step 3: Two parallel lines cut by a transversal** For our safety, it is important that drivers recognize a stop sign immediately. Stop signs are made with exact side and angle measurements to form a regular octagon. They are red so they are easy to see. The three lines drawn below are straight lines. Lines **a** and **b** are parallel. ### Diagram Explanation: The diagram features two parallel lines labeled **a** and **b**, with a red octagonal stop sign placed between them. These lines are intersected by a transversal line labeled **c**. Several points are marked at the intersections: - Point **H** is where the transversal **c** intersects the upper parallel line **a**. - Point **G** is directly where line **a** intersects the edge of the stop sign. - Point **F** is above the stop sign where the letter 'O' appears. - Point **E** is toward the top just above where the transversal **c** starts. - Point **L** is where the transversal **c** intersects the lower parallel line **b**. - Points **I** and **J** are at the intersections where line **b** crosses just below the stop sign. - Point **K** is along the line **c** between points **L** and **J**. The arrows at the end of the parallel lines **a** and **b** indicate that they extend infinitely in the directions shown. This diagram visually reinforces the concept of parallel lines being consistently the same distance apart and intersected by a transversal, creating specific angle relationships, which help drivers recognize traffic signs efficiently.
**Geometry Problem Set Based on a Regular Octagon Stop Sign** **Diagram Explanation:** The given image shows a top view of a stop sign, which is described as a regular octagon. The stop sign sits on top of a post, and several angles are marked around this intersection. Specifically, angles ∠F, ∠L, ∠E, ∠K, ∠H, and ∠I are highlighted along with segments marked by points L, K, and J. **Questions:** **a) The stop sign is a regular octagon, so the measure of ∠F must be 67.5°. What is the angle measure for ∠L? Describe the relationship between ∠F and ∠L.** **b) What is the measure of ∠E? Explain how you know.** **c) Describe the relationship between ∠E and ∠K. What is the measure of ∠K?** **d) What is the measure of ∠H? Explain.** **e) What is the measure of ∠I? Explain.** **f) Describe the relationship between ∠H and ∠L.** --- **Answers:** **a)** The stop sign is a regular octagon, thus each internal angle of the octagon would be 135°. Given that ∠F is an external angle and is equal to 67.5°, the corresponding internal angle ∠L would be: ∠L = 180° - 67.5° = 112.5° Therefore, ∠L measures 112.5°. **b)** To determine the measure of ∠E, we need to understand that the internal angles of an octagon add up to 1080° (since (n-2) × 180° for an n-sided polygon). The measure of each internal angle in a regular octagon (as provided) is 135°. Therefore, assuming the point on the octagon that relates to ∠E is part of this angle, ∠E = 135°. **c)** The relationship between ∠E and ∠K can be described if we consider ∠K as an external angle. If ∠E = 135° (an internal angle of the octagon), the external angle ∠K would be: ∠K = 180° - 135°
Transcribed Image Text:**Geometry Problem Set Based on a Regular Octagon Stop Sign** **Diagram Explanation:** The given image shows a top view of a stop sign, which is described as a regular octagon. The stop sign sits on top of a post, and several angles are marked around this intersection. Specifically, angles ∠F, ∠L, ∠E, ∠K, ∠H, and ∠I are highlighted along with segments marked by points L, K, and J. **Questions:** **a) The stop sign is a regular octagon, so the measure of ∠F must be 67.5°. What is the angle measure for ∠L? Describe the relationship between ∠F and ∠L.** **b) What is the measure of ∠E? Explain how you know.** **c) Describe the relationship between ∠E and ∠K. What is the measure of ∠K?** **d) What is the measure of ∠H? Explain.** **e) What is the measure of ∠I? Explain.** **f) Describe the relationship between ∠H and ∠L.** --- **Answers:** **a)** The stop sign is a regular octagon, thus each internal angle of the octagon would be 135°. Given that ∠F is an external angle and is equal to 67.5°, the corresponding internal angle ∠L would be: ∠L = 180° - 67.5° = 112.5° Therefore, ∠L measures 112.5°. **b)** To determine the measure of ∠E, we need to understand that the internal angles of an octagon add up to 1080° (since (n-2) × 180° for an n-sided polygon). The measure of each internal angle in a regular octagon (as provided) is 135°. Therefore, assuming the point on the octagon that relates to ∠E is part of this angle, ∠E = 135°. **c)** The relationship between ∠E and ∠K can be described if we consider ∠K as an external angle. If ∠E = 135° (an internal angle of the octagon), the external angle ∠K would be: ∠K = 180° - 135°
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