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.
Angle 5 is 115°
and lines M
and N
are parallel. Find the measure of angle 2.

(1 point)
Responses

115°
115 degrees

75°
75 degrees

65°
65 degrees

180°

Answer 1

wrong

Answer 2

To find the measure of angle 2, we first note the relationships between the angles formed by the transversal intersecting the parallel lines M and N.

Since angle 5 is given as 115° and the lines M and N are parallel, we can utilize the concept of corresponding angles, alternate interior angles, and supplementary angles.

1. **Angles on the same side of the transversal and in the same position**: Angle 5 (at upper N) and angle 2 (at upper M) are corresponding angles. Therefore, angle 2 is equal to angle 5.

Thus, the measure of angle 2 is:
\[
\text{Angle 2} = \text{Angle 5} = 115^\circ
\]

So the correct answer is:
**115°**

Answer 3

I apologize for the oversight. Let's analyze the situation carefully.

You have two parallel lines, M and N, and a transversal that intersects them, forming several angles. The angles at the intersection with line M are labeled 1, 2, 4, and 3 (clockwise starting from the upper left), and the angles at the intersection with line N are labeled 5, 6, 8, and 7 (also starting from the upper left).

Given the information:
- Angle 5 is 115°,
- Angles on the same side of the transversal but opposite lines are supplementary.

To find the relationships between these angles:
- Angle 5 (115°) and angle 8 (which is corresponding to angle 5 but on line M) are also supplementary because they are on the same side of the transversal:
\[
\text{Angle 8} = 180° - 115° = 65°
\]

- Angle 2 (on line M) and Angle 8 (on line N) are alternate interior angles. Therefore,
\[
\text{Angle 2} = \text{Angle 8} = 65°
\]

Thus, the correct answer for angle 2 is **65°**. Thank you for your patience, and I apologize for the confusion in my previous response.