When parallel lines are cut by a transversal, several important angle relationships are formed:
1. **Vertical angles** are the angles that are opposite each other when two lines intersect. They are always congruent (equal in measure).
2. **Alternate interior angles** are the pairs of angles on opposite sides of the transversal but inside the two lines. These angles are also always congruent in the case of a transversal intersecting parallel lines.
3. **Corresponding angles** are the pairs of angles that are in similar positions relative to the two parallel lines and the transversal. They are also congruent when the lines are parallel.
4. **Alternate exterior angles** are the pairs of angles on opposite sides of the transversal but outside the two lines. They are congruent when the lines are parallel.
Since you've mentioned that angle 1 and angle 5 are formed around the intersections of an inclined transversal with two vertical parallel lines (upper M and upper N), we can determine their relationship based on the definitions above. Angle 1 is in the upper left quadrant around the intersection with upper M, and angle 5 is in the upper left quadrant around the intersection with upper N.
Based on their positions and the fact that upper M and upper N are parallel, angle 1 and angle 5 are **corresponding angles**, and as such, they are equal when the lines are parallel. Hence, the relationship between angle 5 and angle 1 is that they are corresponding angles.
Use the figure to answer the question.
An inclined transversal passes through two vertical parallel lines labeled upper M and upper N. The angles formed around the intersection point of upper M are labeled clockwise, starting from the upper left quadrant: 1, 2, 4, and 3. The corresponding angles formed around the intersection point of upper N are labeled clockwise, starting from the upper left quadrant: 5, 6, 8, and 7.
Using facts about the angles formed when parallel lines are cut by a transversal, what relationship can you establish between angle 5 and angle 1?(1 point)
Responses
vertical angles
vertical angles
alternate interior angles
alternate interior angles
corresponding angles
corresponding angles
alternate exterior angles
9 answers
Use the figure to answer the question.
An inclined transversal passes through two vertical parallel lines labeled upper M and upper N. The angles formed around the intersection point of upper M are labeled clockwise, starting from the upper left quadrant: 1, 2, 4, and 3. The corresponding angles formed around the intersection point of upper N are labeled clockwise, starting from the upper left quadrant: 5, 6, 8, and 7.
What is the relationship between angle 3 and angle 6?
(1 point)
Responses
alternate interior angles
alternate interior angles
alternate exterior angles
alternate exterior angles
vertical angles
vertical angles
corresponding angles
corresponding angles
An inclined transversal passes through two vertical parallel lines labeled upper M and upper N. The angles formed around the intersection point of upper M are labeled clockwise, starting from the upper left quadrant: 1, 2, 4, and 3. The corresponding angles formed around the intersection point of upper N are labeled clockwise, starting from the upper left quadrant: 5, 6, 8, and 7.
What is the relationship between angle 3 and angle 6?
(1 point)
Responses
alternate interior angles
alternate interior angles
alternate exterior angles
alternate exterior angles
vertical angles
vertical angles
corresponding angles
corresponding angles
The relationship between angle 3 and angle 6 is that they are alternate interior angles.
When two parallel lines (in this case, lines M and N) are cut by a transversal, the angles that are on opposite sides of the transversal and inside the two parallel lines are called alternate interior angles. In the scenario provided, angle 3 is inside the parallel lines on one side of the transversal, and angle 6 is inside on the opposite side. Therefore, angle 3 and angle 6 are alternate interior angles and are congruent when the lines M and N are parallel.
When two parallel lines (in this case, lines M and N) are cut by a transversal, the angles that are on opposite sides of the transversal and inside the two parallel lines are called alternate interior angles. In the scenario provided, angle 3 is inside the parallel lines on one side of the transversal, and angle 6 is inside on the opposite side. Therefore, angle 3 and angle 6 are alternate interior angles and are congruent when the lines M and N are parallel.
Use the figure to answer the question.
Two intersecting lines form an x and have four angles at the point of intersection labeled clockwise from the top: 1, 2, 3, and 4.
If angle 1 in the picture is 63°, what is the measure of angle 3? Why?
(1 point)
Responses
Angle 3 is 63° because angle 1 and angle 3 are vertical angles.
Angle 3 is 63 degrees because angle 1 and angle 3 are vertical angles.
Angle 3 is 117° because angle 1 and angle 3 form a line.
Angle 3 is 117 degrees because angle 1 and angle 3 form a line.
Angle 3 is 63° because angle 1 and angle 3 are corresponding angles.
Angle 3 is 63 degrees because angle 1 and angle 3 are corresponding angles.
There is not enough information in the figure to establish this.
Two intersecting lines form an x and have four angles at the point of intersection labeled clockwise from the top: 1, 2, 3, and 4.
If angle 1 in the picture is 63°, what is the measure of angle 3? Why?
(1 point)
Responses
Angle 3 is 63° because angle 1 and angle 3 are vertical angles.
Angle 3 is 63 degrees because angle 1 and angle 3 are vertical angles.
Angle 3 is 117° because angle 1 and angle 3 form a line.
Angle 3 is 117 degrees because angle 1 and angle 3 form a line.
Angle 3 is 63° because angle 1 and angle 3 are corresponding angles.
Angle 3 is 63 degrees because angle 1 and angle 3 are corresponding angles.
There is not enough information in the figure to establish this.
Angle 3 is 63° because angle 1 and angle 3 are vertical angles.
When two lines intersect, they form two pairs of vertical angles. These angles are opposite each other at the point of intersection. Vertical angles are always congruent, which means they have the same measure. Since angle 1 is given as 63°, angle 3, which is the vertical angle opposite to angle 1, must also be 63°.
When two lines intersect, they form two pairs of vertical angles. These angles are opposite each other at the point of intersection. Vertical angles are always congruent, which means they have the same measure. Since angle 1 is given as 63°, angle 3, which is the vertical angle opposite to angle 1, must also be 63°.
Calculate the supplement of an angle that measures 85°.(1 point)
Responses
The supplement of the angle is 5° because 90°−85°=5°.
The supplement of the angle is 5 degrees because 90 degrees minus 85 degrees equals 5 degrees .
The supplement is 95° because 180°−85°=95°.
The supplement is 95 degrees because 180 degrees minus 85 degrees equals 95 degrees .
The supplement of the angle is −95° because 85°−180°=−95°.
The supplement of the angle is negative 95 degrees because 85 degrees minus 180 degrees equals negative 95 degrees .
The supplement of the angle is 85° because supplementary angles are congruent.
Responses
The supplement of the angle is 5° because 90°−85°=5°.
The supplement of the angle is 5 degrees because 90 degrees minus 85 degrees equals 5 degrees .
The supplement is 95° because 180°−85°=95°.
The supplement is 95 degrees because 180 degrees minus 85 degrees equals 95 degrees .
The supplement of the angle is −95° because 85°−180°=−95°.
The supplement of the angle is negative 95 degrees because 85 degrees minus 180 degrees equals negative 95 degrees .
The supplement of the angle is 85° because supplementary angles are congruent.
The supplement of an angle is the angle that, when added to the original angle, equals 180°. To calculate the supplement of an angle that measures 85°:
The supplement is 95° because 180° − 85° = 95°.
So the correct response is:
The supplement is 95 degrees because 180 degrees minus 85 degrees equals 95 degrees.
The supplement is 95° because 180° − 85° = 95°.
So the correct response is:
The supplement is 95 degrees because 180 degrees minus 85 degrees equals 95 degrees.
Use the image to answer the question.
A diagram shows two horizontal parallel lines labeled m and n. They are intersected by an upward diagonal line that is labeled transversal. All three lines have arrows at both ends. The eight angles formed by the transversal are labeled 1 to 8. The angles formed by the intersection of the transversal and m are labeled 1, 2 above line m, and 3, 4 below. The angles formed by the intersection of the transversal and n is labeled 5, 6, above line n, and 7, 8 below. The text at the bottom reads lines m and n are parallel lines.
Which angles are congruent to ∠4?
(1 point)
Responses
∠2 is congruent to ∠4.
angle 2 is congruent to angle 4 .
∠5 is congruent to ∠4.
angle 5 is congruent to angle 4 .
∠1 is congruent to ∠4.
angle 1 is congruent to angle 4 .
∠1, ∠5 and ∠8 are congruent to ∠4.
A diagram shows two horizontal parallel lines labeled m and n. They are intersected by an upward diagonal line that is labeled transversal. All three lines have arrows at both ends. The eight angles formed by the transversal are labeled 1 to 8. The angles formed by the intersection of the transversal and m are labeled 1, 2 above line m, and 3, 4 below. The angles formed by the intersection of the transversal and n is labeled 5, 6, above line n, and 7, 8 below. The text at the bottom reads lines m and n are parallel lines.
Which angles are congruent to ∠4?
(1 point)
Responses
∠2 is congruent to ∠4.
angle 2 is congruent to angle 4 .
∠5 is congruent to ∠4.
angle 5 is congruent to angle 4 .
∠1 is congruent to ∠4.
angle 1 is congruent to angle 4 .
∠1, ∠5 and ∠8 are congruent to ∠4.
When two parallel lines (in this case, lines m and n) are intersected by a transversal, several pairs of congruent angles are formed:
1. **Alternate Interior Angles** are on opposite sides of the transversal and interior to the parallel lines. They are congruent.
2. **Corresponding Angles** are in the same relative position at each intersection where the transversal crosses the parallel lines. They are congruent.
3. **Alternate Exterior Angles** are on opposite sides of the transversal and exterior to the parallel lines. They are congruent.
Since line m and line n are parallel, and we're looking for angles congruent to ∠4:
- ∠4 and ∠2 are **same-side interior angles** and are supplementary (not congruent) with each other.
- ∠4 and ∠5 are **corresponding angles** and are congruent.
- ∠4 and ∠1 are on the opposite sides of the transversal but outside the parallel lines, which makes them **alternate exterior angles**, and they are congruent.
- ∠4 and ∠8 are at the opposite intersections and on the same side of the transversal but interior to the parallel lines, which makes them **alternate interior angles** with respect to angles formed at the other intersection. Therefore, they are congruent as well.
So the correct response is:
∠1, ∠5, and ∠8 are congruent to ∠4.
1. **Alternate Interior Angles** are on opposite sides of the transversal and interior to the parallel lines. They are congruent.
2. **Corresponding Angles** are in the same relative position at each intersection where the transversal crosses the parallel lines. They are congruent.
3. **Alternate Exterior Angles** are on opposite sides of the transversal and exterior to the parallel lines. They are congruent.
Since line m and line n are parallel, and we're looking for angles congruent to ∠4:
- ∠4 and ∠2 are **same-side interior angles** and are supplementary (not congruent) with each other.
- ∠4 and ∠5 are **corresponding angles** and are congruent.
- ∠4 and ∠1 are on the opposite sides of the transversal but outside the parallel lines, which makes them **alternate exterior angles**, and they are congruent.
- ∠4 and ∠8 are at the opposite intersections and on the same side of the transversal but interior to the parallel lines, which makes them **alternate interior angles** with respect to angles formed at the other intersection. Therefore, they are congruent as well.
So the correct response is:
∠1, ∠5, and ∠8 are congruent to ∠4.
3 answers