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Triangles Online Practice
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Question
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.

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

(1 point)
Responses

115°
115 degrees

65°
65 degrees

180°
180 degrees

75°
75 degrees
Remaining Attempts : 3
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Answer 1

To find the measure of angle 2, we can use the properties of angles formed by a transversal intersecting two parallel lines.

Given that angle 5 is \(115^\circ\), we can determine the measures of the other angles formed.

**Properties of Angles:**
1. Corresponding angles: Angles that occupy the same relative position at each intersection where a straight line crosses two others. These angles are equal.
2. Alternate interior angles: Angles that are on opposite sides of the transversal and inside the parallel lines. These angles are equal.
3. Same-side interior angles: Angles that are on the same side of the transversal and inside the parallel lines. These angles are supplementary (i.e., they sum to \(180^\circ\)).

From the description, we can determine:
- Angle 5 (which is \(115^\circ\)) and angle 6 are corresponding angles, thus angle 6 = \(115^\circ\).
- Angle 2 is a corresponding angle to angle 6.

Since angle 2 and angle 6 are corresponding, angle 2 also measures \(115^\circ\).

So, the correct response is:

**115°**