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27. Find each of the specified angles related to the pentagon in the following picture. Assume that the arrows indicate two parallel lines. Provide a short explanation for how you found each angle. angle A = angle B = angle C = angle D = angle E = B 70° A D с 50° 80° E

27. Find each of the specified angles related to the pentagon in the following picture. Assume that the arrows indicate two parallel lines. Provide a short explanation for how you found each angle. angle A = angle B = angle C = angle D = angle E = B 70° A D с 50° 80° E

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter12: Angle Relationships And Transformations
Section12.2: Angles And Parallel Lines
Problem 13E
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Question
**Problem Statement:** 27. Find each of the specified angles related to the pentagon in the following picture. Assume that the arrows indicate two parallel lines. Provide a short explanation for how you found each angle. - Angle A = - Angle B = - Angle C = - Angle D = - Angle E = **Diagram Description:** A diagram is provided with two parallel lines intersected by a transversal. Labels and angle measures are indicated as follows: - The top horizontal line has an angle marked \(70^\circ\) at the top-left side of point A. - Moving to the right on the top horizontal line, an interior angle \(50^\circ\) is given at point C. - Approximately diagonally downward, point E is marked with an angle of \(80^\circ\) on the right side of point D. - The bottom is horizontally parallel to the top horizontal line, with points B and D lying on it. **Explanations and Solutions:** 1. **Angle A:** - Given that the top and bottom lines are parallel, and the 70° is corresponding to angle A (since corresponding angles are equal when the lines are parallel), hence: - \( \text{Angle A} = 70^\circ \) 2. **Angle B:** - Angle B and angle A are also corresponding angles as both the parallel lines are intersected by a transversal. Angle B is thus equal to angle A: - \( \text{Angle B} = 70^\circ \) 3. **Angle C:** - Angle C is given as \(50^\circ\). 4. **Angle D:** - Angle D forms a linear pair with angle C, making them supplementary angles (the sum is \(180^\circ\)). Therefore: - \( \text{Angle D} = 180^\circ - 50^\circ \) - \( \text{Angle D} = 130^\circ \) 5. **Angle E:** - Angle E is given as \(80^\circ\). By applying properties of parallel lines and angles (corresponding, supplementary), we can determine the measure of each specified angle in relation to the given parallel lines and angles.
Transcribed Image Text:**Problem Statement:** 27. Find each of the specified angles related to the pentagon in the following picture. Assume that the arrows indicate two parallel lines. Provide a short explanation for how you found each angle. - Angle A = - Angle B = - Angle C = - Angle D = - Angle E = **Diagram Description:** A diagram is provided with two parallel lines intersected by a transversal. Labels and angle measures are indicated as follows: - The top horizontal line has an angle marked \(70^\circ\) at the top-left side of point A. - Moving to the right on the top horizontal line, an interior angle \(50^\circ\) is given at point C. - Approximately diagonally downward, point E is marked with an angle of \(80^\circ\) on the right side of point D. - The bottom is horizontally parallel to the top horizontal line, with points B and D lying on it. **Explanations and Solutions:** 1. **Angle A:** - Given that the top and bottom lines are parallel, and the 70° is corresponding to angle A (since corresponding angles are equal when the lines are parallel), hence: - \( \text{Angle A} = 70^\circ \) 2. **Angle B:** - Angle B and angle A are also corresponding angles as both the parallel lines are intersected by a transversal. Angle B is thus equal to angle A: - \( \text{Angle B} = 70^\circ \) 3. **Angle C:** - Angle C is given as \(50^\circ\). 4. **Angle D:** - Angle D forms a linear pair with angle C, making them supplementary angles (the sum is \(180^\circ\)). Therefore: - \( \text{Angle D} = 180^\circ - 50^\circ \) - \( \text{Angle D} = 130^\circ \) 5. **Angle E:** - Angle E is given as \(80^\circ\). By applying properties of parallel lines and angles (corresponding, supplementary), we can determine the measure of each specified angle in relation to the given parallel lines and angles.
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