If M

Question

M
and N
N
are parallel and angle 1 is 135°
135
°
, what is the measure of angle 7?(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

Given that lines \( M \) and \( N \) are parallel and angle 1 measures \( 135^\circ \), we can determine the measure of angle 7 using the properties of parallel lines and transversals.

1. Angle 1 and angle 5 are corresponding angles because they are both formed by the transversal intersecting the two parallel lines. Since corresponding angles are equal when two lines are parallel, we have: \[ \text{Angle 5} = \text{Angle 1} = 135^\circ \]

2. Angles 5 and 7 are also supplementary because they are on a straight line formed by the transversal at line \( N \). Therefore: \[ \text{Angle 5} + \text{Angle 7} = 180^\circ \]

   Substituting the measure of angle 5: \[ 135^\circ + \text{Angle 7} = 180^\circ \]

3. Solving for angle 7: \[ \text{Angle 7} = 180^\circ - 135^\circ = 45^\circ \]

Thus, the measure of angle 7 is \( \boxed{45^\circ} \).