What number could replace the □?
2 answers:
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Answers:
1. Angle 5 and angle 11
5. Angle 4 and angle 6
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Explanations:
Let's go through the list of possible choices and check each one.
For each of these, I'll refer to the attached image.
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1. Angle 5 and angle 11
Note how I labeled the lines A through D (as well as color-coded them). Imagine if line A and line B were made to be parallel lines. Line D is the transversal cut that helps generate angle 5 and angle 11. We'll be focusing on this tranversal. Ignore line C entirely for now.
We can see that angle 5 and angle 11 are on the outside of the "parallel" train tracks that A and B form. That makes them exterior angles. The two angles are on alternate sides of the transversal cut line D. All together, they are alternate exterior angles.
This is one of the answers
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2. Angle 7 and angle 12
Again focus on only line A, B, and D. Ignore line C. Angle 12 is exterior but angle 7 is an interior angle. It is between the two "parallel" train tracks line A and line B.
Cross this off the list.
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3. Angle 11 and angle 16
This time we'll imagine that line C and line D can be rearranged to be parallel. Line B is the transversal cut we want. Ignore line A entirely.
Angle 16 and angle 11 are exterior angles with regards to the lines mentioned above; however, they do not alternate on opposite sides of line B. These two angles are same side exterior angles.
Cross this off the list.
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4. Angle 2 and angle 14
These two angles are corresponding angles. Imagine line A and B are laid parallel with line C as the transversal cut.
Angle 2 and angle 14 are on the same side of the transversal cut. The two angles are both above their adjacent line (A and B)
Cross this off the list.
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5. Angle 4 and angle 6
Imagine that line C and line D can be rearranged to be parallel. Line A is the transversal cut we want. Ignore line B entirely.
Based on that set up, we can see that angle 4 and angle 6 are indeed alternate exterior angles.
This is one of the answers
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6. Angle 8 and angle 10
These are alternate interior angles. It might help to erase line C. It might also help to arrange line A to be parallel to line B.
Cross this off the list.
1. Angle 5 and angle 11
5. Angle 4 and angle 6
================================================
Explanations:
Let's go through the list of possible choices and check each one.
For each of these, I'll refer to the attached image.
-------------------------
1. Angle 5 and angle 11
Note how I labeled the lines A through D (as well as color-coded them). Imagine if line A and line B were made to be parallel lines. Line D is the transversal cut that helps generate angle 5 and angle 11. We'll be focusing on this tranversal. Ignore line C entirely for now.
We can see that angle 5 and angle 11 are on the outside of the "parallel" train tracks that A and B form. That makes them exterior angles. The two angles are on alternate sides of the transversal cut line D. All together, they are alternate exterior angles.
This is one of the answers
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2. Angle 7 and angle 12
Again focus on only line A, B, and D. Ignore line C. Angle 12 is exterior but angle 7 is an interior angle. It is between the two "parallel" train tracks line A and line B.
Cross this off the list.
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3. Angle 11 and angle 16
This time we'll imagine that line C and line D can be rearranged to be parallel. Line B is the transversal cut we want. Ignore line A entirely.
Angle 16 and angle 11 are exterior angles with regards to the lines mentioned above; however, they do not alternate on opposite sides of line B. These two angles are same side exterior angles.
Cross this off the list.
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4. Angle 2 and angle 14
These two angles are corresponding angles. Imagine line A and B are laid parallel with line C as the transversal cut.
Angle 2 and angle 14 are on the same side of the transversal cut. The two angles are both above their adjacent line (A and B)
Cross this off the list.
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5. Angle 4 and angle 6
Imagine that line C and line D can be rearranged to be parallel. Line A is the transversal cut we want. Ignore line B entirely.
Based on that set up, we can see that angle 4 and angle 6 are indeed alternate exterior angles.
This is one of the answers
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6. Angle 8 and angle 10
These are alternate interior angles. It might help to erase line C. It might also help to arrange line A to be parallel to line B.
Cross this off the list.