Use the figure to answer the question.

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

alternate interior angles
alternate interior angles

alternate exterior angles
alternate exterior angles

corresponding angles
corresponding angles

vertical angles
vertical angles
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Answer 1

To establish the relationship between angle 5 and angle 1, we can analyze their positions relative to the parallel lines M and N, and the transversal.

• Angle 1 is located on the upper left side of line M.
• Angle 5 is located on the upper left side of line N, which is parallel to line M.

Since angle 1 is located above line M and angle 5 is located above line N, this places them both above their respective lines, but in different sections relative to the transversal.

The correct relationship is that angle 5 and angle 1 are corresponding angles. Corresponding angles are formed when a transversal intersects two parallel lines and are located in the same position relative to the lines.

Therefore, the correct answer is:

corresponding angles.

Answer 2

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

corresponding angles
corresponding angles

alternate interior angles
alternate interior angles

alternate exterior angles
alternate exterior angles

vertical angles
vertical angles
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Answer 3

To determine the relationship between angle 3 and angle 6, we can analyze their positions relative to the transversal and the two parallel lines (M and N).

• Angle 3 is located on the lower right side of line M.
• Angle 6 is located on the lower right side of line N.

Both angles are on the same side of the transversal and in different parallel lines, which means they are in corresponding positions relative to the lines.

Thus, angle 3 and angle 6 are corresponding angles.

Therefore, the correct answer is:

corresponding angles.

Answer 4

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 vertical angles.
Angle 3 is 63 degrees because angle 1 and angle 3 are vertical angles.

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.
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Answer 5

To determine the measure of angle 3 when angle 1 is 63°, we need to analyze the relationship between these two angles:

• Angle 1 and angle 3 are formed by two intersecting lines, which means they are positioned on opposite sides of the intersection point.
• Angles at the intersection of two lines also follow the property that any pair of angles that are linear (adjacent angles that form a straight line) add up to 180°.

Since angle 1 (63°) and angle 3 are on opposite sides of the intersection and form a line, they are supplementary angles.

Thus, we can calculate angle 3 as follows:

\[ \text{Angle 3} + \text{Angle 1} = 180° \] \[ \text{Angle 3} + 63° = 180° \] \[ \text{Angle 3} = 180° - 63° = 117° \]

Therefore, the correct response is:

Angle 3 is 117° because angle 1 and angle 3 form a line.

Answer 6

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 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 the angle is 85 degrees because supplementary angles are congruent.

The supplement is 95° because 180°−85°=95°.

Answer 7

The supplement of an angle is calculated by subtracting the angle from 180°.

For an angle measuring 85°:

\[ \text{Supplement} = 180° - 85° = 95° \]

Thus, the correct response is:

The supplement is 95° because 180°−85°=95°.