Common Core: 8th Grade Math : Use Informal Arguments to Establish Facts about the Angle Sum and Exterior Angle of Triangles: CCSS.Math.Content.8.G.A.5

Study concepts, example questions & explanations for Common Core: 8th Grade Math

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Example Questions

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Example Question #1 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

The image provided contains a set of parallel lines,  and , and a transversal line, . If angle  is equal to , then which of the other angles is equal to 

2

Possible Answers:

Correct answer:

Explanation:

First, we need to define some key terms:

Parallel Lines: Parallel lines are lines that will never intersect with each other. 

Transversal Line: A transversal line is a line that crosses two parallel lines.

In the the image provided, lines  and  are parallel lines and line  is a transversal line because it crosses the two parallel lines.

It is important to know that transversal lines create angle relationships:

  • Vertical angles are congruent
  • Corresponding angles are congruent
  • Alternate interior angles are congruent
  • Alternate exterior angles are congruent

Let's look at angle  in the image provided below to demonstrate our relationships. 

1

Angle  and  are vertical angles.

Angle  and  are corresponding angles. 

Angle  and  are exterior angles. 

Angle  is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs  and  as well as angle  and 

For this problem, we want to find the angle that is congruent to angle . Based on our answer choices, angle  and  are vertical angles; thus, both angle  and  are congruent and equal 

Example Question #2 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

The image provided contains a set of parallel lines,  and , and a transversal line, . If angle  is equal to , then which of the other angles is equal to 

2

 

Possible Answers:

Correct answer:

Explanation:

First, we need to define some key terms:

Parallel Lines: Parallel lines are lines that will never intersect with each other. 

Transversal Line: A transversal line is a line that crosses two parallel lines.

In the the image provided, lines  and  are parallel lines and line  is a transversal line because it crosses the two parallel lines.

It is important to know that transversal lines create angle relationships:

  • Vertical angles are congruent
  • Corresponding angles are congruent
  • Alternate interior angles are congruent
  • Alternate exterior angles are congruent

Let's look at angle  in the image provided below to demonstrate our relationships. 

1

Angle  and  are vertical angles.

Angle  and  are corresponding angles. 

Angle  and  are exterior angles. 

Angle  is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs  and  as well as angle  and 

For this problem, we want to find the angle that is congruent to angle . Based on our answer choices, angle  and  are vertical angles; thus, both angle  and  are congruent and equal 

Example Question #3 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

The image provided contains a set of parallel lines,  and , and a transversal line, . If angle  is equal to , then which of the other angles is equal to 

2

 

Possible Answers:

Correct answer:

Explanation:

First, we need to define some key terms:

Parallel Lines: Parallel lines are lines that will never intersect with each other. 

Transversal Line: A transversal line is a line that crosses two parallel lines.

In the the image provided, lines  and  are parallel lines and line  is a transversal line because it crosses the two parallel lines.

It is important to know that transversal lines create angle relationships:

  • Vertical angles are congruent
  • Corresponding angles are congruent
  • Alternate interior angles are congruent
  • Alternate exterior angles are congruent

Let's look at angle  in the image provided below to demonstrate our relationships. 

1

Angle  and  are vertical angles.

Angle  and  are corresponding angles. 

Angle  and  are exterior angles. 

Angle  is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs  and  as well as angle  and 

For this problem, we want to find the angle that is congruent to angle . Based on our answer choices, angle  and  are corresponding angles; thus, both angle  and  are congruent and equal 

Example Question #4 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

The image provided contains a set of parallel lines,  and , and a transversal line, . If angle  is equal to , then which of the other angles is equal to 

2

 

 

Possible Answers:

Correct answer:

Explanation:

First, we need to define some key terms:

Parallel Lines: Parallel lines are lines that will never intersect with each other. 

Transversal Line: A transversal line is a line that crosses two parallel lines.

In the the image provided, lines  and  are parallel lines and line  is a transversal line because it crosses the two parallel lines.

It is important to know that transversal lines create angle relationships:

  • Vertical angles are congruent
  • Corresponding angles are congruent
  • Alternate interior angles are congruent
  • Alternate exterior angles are congruent

Let's look at angle  in the image provided below to demonstrate our relationships. 

1

Angle  and  are vertical angles.

Angle  and  are corresponding angles. 

Angle  and  are exterior angles. 

Angle  is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs  and  as well as angle  and 

For this problem, we want to find the angle that is congruent to angle . Based on our answer choices, angle  and  are corresponding angles; thus, both angle  and  are congruent and equal 

Example Question #5 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

The image provided contains a set of parallel lines,  and , and a transversal line, . If angle  is equal to , then which of the other angles is equal to 

2

 

Possible Answers:

Correct answer:

Explanation:

First, we need to define some key terms:

Parallel Lines: Parallel lines are lines that will never intersect with each other. 

Transversal Line: A transversal line is a line that crosses two parallel lines.

In the the image provided, lines  and  are parallel lines and line  is a transversal line because it crosses the two parallel lines.

It is important to know that transversal lines create angle relationships:

  • Vertical angles are congruent
  • Corresponding angles are congruent
  • Alternate interior angles are congruent
  • Alternate exterior angles are congruent

Let's look at angle  in the image provided below to demonstrate our relationships. 

1

Angle  and  are vertical angles.

Angle  and  are corresponding angles. 

Angle  and  are exterior angles. 

Angle  is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs  and  as well as angle  and 

For this problem, we want to find the angle that is congruent to angle . Based on our answer choices, angle  and  are alternate exterior angles; thus, both angle  and  are congruent and equal 

Example Question #6 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

The image provided contains a set of parallel lines,  and , and a transversal line, . If angle  is equal to , then which of the other angles is equal to 

2

 

 

Possible Answers:

Correct answer:

Explanation:

First, we need to define some key terms:

Parallel Lines: Parallel lines are lines that will never intersect with each other. 

Transversal Line: A transversal line is a line that crosses two parallel lines.

In the the image provided, lines  and  are parallel lines and line  is a transversal line because it crosses the two parallel lines.

It is important to know that transversal lines create angle relationships:

  • Vertical angles are congruent
  • Corresponding angles are congruent
  • Alternate interior angles are congruent
  • Alternate exterior angles are congruent

Let's look at angle  in the image provided below to demonstrate our relationships. 

1

Angle  and  are vertical angles.

Angle  and  are corresponding angles. 

Angle  and  are exterior angles. 

Angle  is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs  and  as well as angle  and 

For this problem, we want to find the angle that is congruent to angle . Based on our answer choices, angle  and  are alternate exterior angles; thus, both angle  and  are congruent and equal 

Example Question #7 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

The image provided contains a set of parallel lines,  and , and a transversal line, . If angle  is equal to , then which of the other angles is equal to 

2

 

Possible Answers:

Correct answer:

Explanation:

First, we need to define some key terms:

Parallel Lines: Parallel lines are lines that will never intersect with each other. 

Transversal Line: A transversal line is a line that crosses two parallel lines.

In the the image provided, lines  and  are parallel lines and line  is a transversal line because it crosses the two parallel lines.

It is important to know that transversal lines create angle relationships:

  • Vertical angles are congruent
  • Corresponding angles are congruent
  • Alternate interior angles are congruent
  • Alternate exterior angles are congruent

Let's look at angle  in the image provided below to demonstrate our relationships. 

1

Angle  and  are vertical angles.

Angle  and  are corresponding angles. 

Angle  and  are exterior angles. 

Angle  is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs  and  as well as angle  and 

For this problem, we want to find the angle that is congruent to angle . Based on our answer choices, angle  and  are alternate interior angles; thus, both angle  and  are congruent and equal 

Example Question #8 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

The image provided contains a set of parallel lines,  and , and a transversal line, . If angle  is equal to , then which of the other angles is equal to 

2

 

 

Possible Answers:

Correct answer:

Explanation:

First, we need to define some key terms:

Parallel Lines: Parallel lines are lines that will never intersect with each other. 

Transversal Line: A transversal line is a line that crosses two parallel lines.

In the the image provided, lines  and  are parallel lines and line  is a transversal line because it crosses the two parallel lines.

It is important to know that transversal lines create angle relationships:

  • Vertical angles are congruent
  • Corresponding angles are congruent
  • Alternate interior angles are congruent
  • Alternate exterior angles are congruent

Let's look at angle  in the image provided below to demonstrate our relationships. 

1

Angle  and  are vertical angles.

Angle  and  are corresponding angles. 

Angle  and  are exterior angles. 

Angle  is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs  and  as well as angle  and 

For this problem, we want to find the angle that is congruent to angle . Based on our answer choices, angle  and  are alternate interior angles; thus, both angle  and  are congruent and equal 

Example Question #9 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

The image provided contains a set of parallel lines,  and , and a transversal line, . Which angle is NOT equal to angle 

2

 

 

Possible Answers:

Correct answer:

Explanation:

First, we need to define some key terms:

Parallel Lines: Parallel lines are lines that will never intersect with each other. 

Transversal Line: A transversal line is a line that crosses two parallel lines.

In the the image provided, lines  and  are parallel lines and line  is a transversal line because it crosses the two parallel lines.

It is important to know that transversal lines create angle relationships:

  • Vertical angles are congruent
  • Corresponding angles are congruent
  • Alternate interior angles are congruent
  • Alternate exterior angles are congruent

Let's look at angle  in the image provided below to demonstrate our relationships. 

1

Angle  and  are vertical angles.

Angle  and  are corresponding angles. 

Angle  and  are exterior angles. 

Angle  is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs  and  as well as angle  and 

For this problem, we want to find the angle that is not equal to to angle . Let's look at our answer choices:

Angle  and  are vertical angles, which means they are congruent. 

Angle  and   are alternate exterior angles, which means they are congruent. 

Angle  and  are corresponding angles, which means they are congruent. 

However, angle  and  do not share a common angle relationship; thus they are not congruent. 

Example Question #10 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

The image provided contains a set of parallel lines,  and , and a transversal line, . Which angle is NOT equal to angle 

2

 

Possible Answers:

Correct answer:

Explanation:

First, we need to define some key terms:

Parallel Lines: Parallel lines are lines that will never intersect with each other. 

Transversal Line: A transversal line is a line that crosses two parallel lines.

In the the image provided, lines  and  are parallel lines and line  is a transversal line because it crosses the two parallel lines.

It is important to know that transversal lines create angle relationships:

  • Vertical angles are congruent
  • Corresponding angles are congruent
  • Alternate interior angles are congruent
  • Alternate exterior angles are congruent

Let's look at angle  in the image provided below to demonstrate our relationships. 

1

Angle  and  are vertical angles.

Angle  and  are corresponding angles. 

Angle  and  are exterior angles. 

Angle  is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs  and  as well as angle  and 

For this problem, we want to find the angle that is not equal to to angle . Let's look at our answer choices:

Angle  and  are vertical angles, which means they are congruent. 

Angle  and   are alternate interior angles, which means they are congruent. 

Angle  and  are corresponding angles, which means they are congruent. 

However, angle  and  do not share a common angle relationship; thus they are not congruent. 

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