If M

Question

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

GPT-4o mini · Answer

Given that lines $M$ and $N$ are parallel and angle $1$ measures $135^\circ$, we can determine the measure of angle $8$ using the properties of parallel lines and transversals. Angle $1$ and angle $8$ are corresponding angles because they are formed by the same transversal and are in corresponding positions relative to the parallel lines $M$ and $N$. For parallel lines cut by a transversal, corresponding angles are equal. Since angle $1$ measures $135^\circ$: $$ \text{Angle } 8 = \text{Angle } 1 = 135^\circ $$ Thus, the measure of angle $8$ is $135^\circ$.