If M

Question

and N
are parallel and angle 1 is 135°
, what is the measure of angle 2?(1 point)

Answer 1

If lines M and N are parallel and angle 1 measures 135°, then angle 2, which is corresponding to angle 1 or an alternate interior angle, will also be affected by the properties of parallel lines.

Assuming angle 2 is one of the angles formed by a transversal intersecting parallel lines M and N, angle 2 will be supplementary to angle 1 if they are on the same side of the transversal.

Thus, if angle 2 is on the same side of the transversal with respect to angle 1, you would use the following calculation:

\[ \text{Angle 2} = 180° - \text{Angle 1} \] \[ \text{Angle 2} = 180° - 135° = 45° \]

If angle 2 is a corresponding or alternate interior angle, then:

\[ \text{Angle 2} = 135° \]

So the exact measure of angle 2 depends on its position relative to angle 1. If it's supplementary, it measures 45°. If it's corresponding or alternate, it measures 135°. Please clarify the positioning if necessary!

Answer 2

If M
and N
are parallel and angle 1 is 135°
, what is the measure of angle 8?(1 point)

Answer 3

To determine the measure of angle 8, we need to understand its relationship with angle 1, considering that lines M and N are parallel.

If we assume that angle 1 (135°) and angle 8 are either corresponding angles, alternate interior angles, or same-side interior angles formed by a transversal intersecting the parallel lines, we can use the properties of these angles:

1. Corresponding Angles: If angle 8 is a corresponding angle to angle 1, then angle 8 = angle 1 = 135°.

2. Alternate Interior Angles: If angle 8 is an alternate interior angle to angle 1, then angle 8 = angle 1 = 135°.

3. Same-Side Interior Angles: If angle 8 is a same-side interior angle with respect to angle 1, then they are supplementary. In this case: \[ \text{Angle 8} = 180° - \text{Angle 1} \] \[ \text{Angle 8} = 180° - 135° = 45° \]

Without a diagram indicating the specific relationship between angle 1 and angle 8, the most common scenarios are either angle 8 measures 135° (if it's corresponding or alternate interior) or 45° (if it's same-side interior). Please specify the positioning of angle 8 relative to angle 1 for a precise answer!

Answer 4

Use the figure to answer the question.

An illustration shows a right inclined transversal passing through two parallel lines labeled upper M and upper N. Four angles are formed at the intersections of the transversal with upper M and upper N.

If M
and N
are parallel and angle 1 is 135°
, what is the sum of angle 6 and angle 8?

(1 point)

Answer 5

Given that lines M and N are parallel and angle 1 measures 135°, we can infer the measures of angles 6 and 8 based on their positions.

Assuming the transversal creates the angles as follows:

• Angle 1 is formed on line M.
• Angles around the transversal include angle 1, angle 2 (which is adjacent to angle 1), angle 6, and angle 8.

Since angle 1 is 135°:

1. Angle 2 (adjacent to angle 1 on the same line) would be supplementary to angle 1: \[ \text{Angle 2} = 180° - 135° = 45° \]

2. Angle 6 and Angle 8:

   • Angle 6 is vertically opposite to angle 2, so: \[ \text{Angle 6} = \text{Angle 2} = 45° \]
   • Angle 8 is on line N and is the corresponding angle to angle 1, so: \[ \text{Angle 8} = \text{Angle 1} = 135° \]

Sum of angle 6 and angle 8: \[ \text{Angle 6} + \text{Angle 8} = 45° + 135° = 180° \]

Thus, the sum of angle 6 and angle 8 is 180°.

Answer 6

Use the figure to answer the question.

An illustration shows a right inclined transversal passing through two parallel lines labeled upper M and upper N. Four angles are formed at the intersections of the transversal with upper M and upper N. The angles formed around the intersection point of the transversal and 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.

Which angle is an alternate interior angle to angle 5?

(1 point)

Answer 7

To identify the alternate interior angle to angle 5 in the given scenario with two parallel lines (M and N) and a transversal, we can visualize or describe the positions of the angles.

1. Angle 5 is located at the upper left intersection of line N with the transversal.
2. The alternate interior angles are the angles that lie between the two parallel lines and are on opposite sides of the transversal.

In this case:

• The position corresponding to angle 5, which is in the upper left quadrant at line N, would have its alternate interior angle located at the lower right quadrant of line M.

From your description of the angles, angle 3 (located at the lower right intersection of line M with the transversal) is the angle that is alternate interior to angle 5.

So, angle 3 is the alternate interior angle to angle 5.

Answer 8

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

corresponding angles
corresponding angles

vertical angles
vertical angles

alternate interior angles
alternate interior angles

alternate exterior angles

Answer 9

To establish the relationship between angle 5 and angle 1 when parallel lines M and N are cut by a transversal, let's analyze their positions:

• Angle 1 is located in the upper left quadrant at the intersection of the transversal with line M.
• Angle 5 is located in the upper left quadrant at the intersection of the transversal with line N.

Since both angles are on the same side of the transversal and both are located in corresponding positions at their respective intersections, we can conclude that:

Angle 5 and angle 1 are corresponding angles.

So, the correct response is: corresponding angles.