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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

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, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . If angle $\angle{\ a}$ is equal to $135^\circ$ , then which of the other angles is equal to $135^\circ?$

Possible Answers:

$\angle{\ d}$

$\angle{\ b}$

$\angle{\ c}$

$\angle{\ f}$

Correct answer:

$\angle{\ c}$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

Angle $\angle{\ a}$ is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs $\angle{\ e}$ and $\angle{\ c}$ as well as angle $\angle{\ d}$ and $\angle{\ f}$ .

For this problem, we want to find the angle that is congruent to angle $\angle{\ a}$ . Based on our answer choices, angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles; thus, both angle $\angle{\ a}$ and $\angle{\ c}$ are congruent and equal $135^\circ$

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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

Possible Answers:

$\angle{\ h}$

$\angle{\ b}$

$\angle{\ e}$

$\angle{\ f}$

Correct answer:

$\angle{\ e}$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

For this problem, we want to find the angle that is congruent to angle $\angle{\ a}$ . Based on our answer choices, angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles; thus, both angle $\angle{\ a}$ and $\angle{\ e}$ are congruent and equal $135^\circ$

Report an Error

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, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . If angle $\angle{\ b}$ is equal to $45^\circ$ , then which of the other angles is equal to $45^\circ$

Possible Answers:

$\angle{\ g}$

$\angle{\ f}$

$\angle{\ c}$

$\angle{\ e}$

Correct answer:

$\angle{\ f}$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

For this problem, we want to find the angle that is congruent to angle $\angle{\ b}$ . Based on our answer choices, angle $\angle{\ b}$ and $\angle{\ f}$ are corresponding angles; thus, both angle $\angle{\ b}$ and $\angle{\ f}$ are congruent and equal $45^\circ$

Report an Error

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

Possible Answers:

$\angle{\ h}$

$\angle{\ f}$

$\angle{\ g}$

$\angle{\ b}$

Correct answer:

$\angle{\ g}$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

For this problem, we want to find the angle that is congruent to angle $\angle{\ a}$ . Based on our answer choices, angle $\angle{\ a}$ and $\angle{\ g}$ are alternate exterior angles; thus, both angle $\angle{\ a}$ and $\angle{\ g}$ are congruent and equal $135^\circ$

Report an Error

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

Possible Answers:

$\angle{\ c}$

$\angle{\ h}$

$\angle{\ a}$

$\angle{\ g}$

Correct answer:

$\angle{\ h}$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

For this problem, we want to find the angle that is congruent to angle $\angle{\ b}$ . Based on our answer choices, angle $\angle{\ b}$ and $\angle{\ h}$ are alternate exterior angles; thus, both angle $\angle{\ b}$ and $\angle{\ h}$ are congruent and equal $45^\circ$

Report an Error

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, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . If angle $\angle{\ c}$ is equal to $135^\circ$ , then which of the other angles is equal to $135^\circ?$

Possible Answers:

$\angle{\ b}$

$\angle{\ h}$

$\angle{\ e}$

$\angle{\ f}$

Correct answer:

$\angle{\ e}$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

For this problem, we want to find the angle that is congruent to angle $\angle{\ c}$ . Based on our answer choices, angle $\angle{\ c}$ and $\angle{\ e}$ are alternate interior angles; thus, both angle $\angle{\ c}$ and $\angle{\ e}$ are congruent and equal $135^\circ$

Report an Error

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, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . If angle $\angle{\ d}$ is equal to $45^\circ$ , then which of the other angles is equal to $45^\circ$

Possible Answers:

$\angle{\ g}$

$\angle{\ a}$

$\angle{\ f}$

$\angle{\ e}$

Correct answer:

$\angle{\ f}$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

For this problem, we want to find the angle that is congruent to angle $\angle{\ d}$ . Based on our answer choices, angle $\angle{\ d}$ and $\angle{\ f}$ are alternate interior angles; thus, both angle $\angle{\ d}$ and $\angle{\ f}$ are congruent and equal $45^\circ$

Report an Error

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, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . Which angle is NOT equal to angle $\angle {\ g}?$

Possible Answers:

$\angle{\ d}$

$\angle{\ c}$

$\angle{\ a}$

$\angle{\ e}$

Correct answer:

$\angle{\ d}$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

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

Angle $\angle{\ g}$ and $\angle{\ e}$ are vertical angles, which means they are congruent.

Angle $\angle{\ g}$ and $\angle{\ a}$ are alternate exterior angles, which means they are congruent.

Angle $\angle{\ g}$ and $\angle{\ c}$ are corresponding angles, which means they are congruent.

However, angle $\angle{\ g}$ and $\angle{\ d}$ do not share a common angle relationship; thus they are not congruent.

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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, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . Which angle is NOT equal to angle $\angle {\ f}?$

Possible Answers:

$\angle{\ c}$

$\angle{\ d}$

$\angle{\ b}$

$\angle{\ h}$

Correct answer:

$\angle{\ c}$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

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

Angle $\angle {\ f}$ and $\angle{\ h}$ are vertical angles, which means they are congruent.

Angle $\angle {\ f}$ and $\angle{\ d}$ are alternate interior angles, which means they are congruent.

Angle $\angle {\ f}$ and $\angle{\ b}$ are corresponding angles, which means they are congruent.

However, angle $\angle {\ f}$ and $\angle{\ c}$ do not share a common angle relationship; thus they are not congruent.

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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, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . Which angle is NOT equal to angle $\angle {\ d}?$

Possible Answers:

$\angle{\ c}$

$\angle{\ f}$

$\angle{\ h}$

$\angle{\ b}$

Correct answer:

$\angle{\ c}$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

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

Angle $\angle{\ d}$ and $\angle{\ b}$ are vertical angles, which means they are congruent.

Angle $\angle{\ d}$ and $\angle{\ f}$ are alternate interior angles, which means they are congruent.

Angle $\angle{\ d}$ and $\angle{\ h}$ are corresponding angles, which means they are congruent.

However, angle $\angle{\ d}$ and $\angle{\ c}$ do not share a common angle relationship; thus they are not congruent.

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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

All Common Core: 8th Grade Math Resources

Example Questions

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

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

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

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

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

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

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

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

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

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

All Common Core: 8th Grade Math Resources

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