Question

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

Answer 1

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

Answer 2

When two parallel lines \( M \) and \( N \) are intersected by a transversal, the angles that are formed have specific relationships. Given that angle 1 measures \( 135^\circ \), we can determine the measure of angle 2 as follows:

- Angle 1 and angle 2 are *consecutive interior angles*. For parallel lines, consecutive interior angles are supplementary, meaning they add up to \( 180^\circ \).

Given:
\[
\text{Angle 1} + \text{Angle 2} = 180^\circ
\]
Substituting the value of angle 1:
\[
135^\circ + \text{Angle 2} = 180^\circ
\]

To find angle 2, we subtract \( 135^\circ \) from \( 180^\circ \):
\[
\text{Angle 2} = 180^\circ - 135^\circ = 45^\circ
\]

Thus, the measure of angle 2 is \( \boxed{45^\circ} \).