Use the figure to answer the question.

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

180°
180 degrees

115°
115 degrees

65°
65 degrees

75°
75 degrees
Remaining Attempts : 3

Answer 1

Given that angle 5 is 115° and lines M and N are parallel, we can analyze the relationships between the angles formed by the transversal.

Since the two lines are parallel, we can use the properties of corresponding and alternate interior angles.

1. Angle 5 is 115°.
2. Angle 6 (which is corresponding to angle 2) will also be 115° because corresponding angles are equal when two parallel lines are cut by a transversal.

Now, to find angle 2, we know that angle 2 is vertically opposite to angle 6, and vertically opposite angles are also equal. Therefore:

• Angle 6 = 115°
• Angle 2 (which is vertically opposite angle 6) = 115°

Thus, the measure of angle 2 is:

115°.