Angles and Parallel Lines Quick Check
2 of 52 of 5 Items
Question
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)
In the described scenario, we have two vertical parallel lines labeled upper M and upper N, and an inclined transversal intersects these lines, forming angles around each intersection. If the angles around upper M are labeled 1, 2, 4, and 3 going clockwise starting from the upper left quadrant, and the corresponding angles around upper N are labeled 5, 6, 8, and 7, we can use the properties of parallel lines and transversals to determine the relationship between angle 3 and angle 6.
Since angle 3 is formed at the intersection with line upper M and angle 6 is formed at the intersection with line upper N:
1. If angle 3 is an interior angle on the right side of the transversal, then angle 6 will be an alternate interior angle with respect to angle 3. Alternate interior angles are equal when the lines are parallel, so angle 3 will be equal to angle 6.
2. If angle 3 is an exterior angle, then angle 6 would not be its alternate interior angle. However, if angle 3 is the consecutive exterior angle to angle 6, they would be supplementary, as consecutive (same-side) exterior angles add up to 180 degrees when the lines are parallel.
Without a diagram, we cannot say for certain which case applies to angles 3 and 6. But typically, in such problems, angle 3 being an interior angle and angle 6 being its alternate interior angle is the expected scenario, making angle 3 and angle 6 equal. To confirm the exact relationship, one would ideally need to view the figure to identify their positions correctly.
Angles and Parallel Lines Quick Check
2 of 52 of 5 Items
Question
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
vertical angles
vertical angles
alternate exterior angles
alternate exterior angles
corresponding angles
corresponding angles
alternate interior angles
alternate interior angles
Based on the pattern of labeling for the angles you've described (angles 1, 2, 4, 3 around the intersection with upper M and angles 5, 6, 8, 7 around the intersection with upper N), and considering that the transversal is inclined passing through the two vertical parallel lines, we can deduce the following relationships:
- Angle 1 corresponds to angle 5.
- Angle 2 corresponds to angle 6.
- Angle 3 corresponds to angle 7.
- Angle 4 corresponds to angle 8.
Given this pattern, angle 3 at the intersection with line upper M is on the same corner and side of the transversal as angle 7 at the intersection with line upper N, making them alternate exterior angles. However, angle 3 in your description corresponds to angle 6 at the intersection with line upper N. This means that angle 3 and angle 6 are corresponding angles, as they are in the same relative position with respect to their respective parallel lines and transversal.
So, the relationship between angle 3 and angle 6 is that they are corresponding angles, and when two lines are parallel (upper M and upper N in this case), their corresponding angles are equal. Therefore, angle 3 equals angle 6.
Angles and Parallel Lines Quick Check
3 of 53 of 5 Items
Question
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
There is not enough information in the figure to establish this.
There is not enough information in the figure to establish this.
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.
Angle 3 is 63° because angle 1 and angle 3 are vertical angles.
When two lines intersect and form an "X" shape, the angles opposite each other are called vertical angles. Vertical angles are congruent, which means they have the same measure.
Given that angle 1 is 63° and angle 3 is the vertical angle to angle 1 (since they are across from each other at the point of intersection), angle 3 will also be 63°.
The correct response is:
Angle 3 is 63° because angle 1 and angle 3 are vertical angles.
Calculate the supplement of an angle that measures 85° .(1 point)
Responses
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 5° because 90°−85°=5°.
The supplement of the angle is 5 degrees because 90 degrees minus 85 degrees equals 5 degrees .
The supplement of the angle is 85° because supplementary angles are congruent.
The supplement of the angle is 85 degrees because supplementary angles are congruent.
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 an angle is what you would add to that angle to get a sum of 180 degrees. To calculate the supplement of an angle that measures 85°, you would subtract the measurement of the angle from 180°:
180° − 85° = 95°
So, the supplement of an angle that measures 85° is 95°.
The correct response is:
The supplement is 95° because 180°−85°=95°.
Angles and Parallel Lines Quick Check
5 of 55 of 5 Items
Question
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
∠5 is congruent to ∠4.
angle 5 is congruent to angle 4 .
∠1, ∠5 and ∠8 are congruent to ∠4.
angle 1 , angle 5 and angle 8 are congruent to angle 4 .
∠1 is congruent to ∠4.
angle 1 is congruent to angle 4 .
∠2 is congruent to ∠4.
In a figure with two parallel lines (labeled m and n) intersected by a transversal, several types of angle relationships can help identify which angles are congruent to ∠4.
Let's go through each pair:
∠5: Since ∠4 is an interior angle on the side of the transversal below line m, ∠5 is also an interior angle but above line n. If ∠4 is the left interior angle at the intersection with line m, then ∠5 would be the corresponding right interior angle at the intersection with line n, so they are not congruent by any standard angle relationships involving parallel lines.
∠1: ∠1 is the alternate exterior angle to ∠4, so they are congruent. When two parallel lines are intersected by a transversal, alternate exterior angles are equal.
∠8: ∠8 is the alternate interior angle to ∠4 (because they are non-adjacent interior angles on opposite sides of the transversal), so they are also congruent. When two parallel lines are intersected by a transversal, alternate interior angles are equal.
∠2: ∠2 would be adjacent to ∠4 and is therefore supplementary to ∠4, making it not congruent to ∠4.
The correct response is that ∠1 and ∠8 are congruent to ∠4. However, the options given do not list ∠1 and ∠8 together, so based on the descriptions, the best available match would be:
∠1, ∠5, and ∠8 are congruent to ∠4.
This choice includes ∠1 and ∠8, which are correct, despite also incorrectly including ∠5. If the test is multiple-choice with only one correct answer, you should select the option that is completely correct or, if such is not provided, the option that matches your best judgment according to standard geometric rules regarding parallel lines and transversals.
So bot is wrong on questions 1 and 2 but besides that they are right.
Answers are:
Question 1: Corresponding angle
Question 2: Alternate exterior angles
Question 3:Angle 3 is 63° because angle 1 and angle 3 are vertical angles.
Question 4: The supplement is 95°
because 180°−85°=95°
Question 5: ∠1, ∠5 and ∠8 are congruent to ∠4