Question

Lines x, y, and z are parallel, and are cut by a transversal w. given m<M=140 , find M<d and m<gLines x, y, and z are parallel, and are cut by a transversal w. given m<M=140 , find M<d and m<g

Answer 1

When lines \( x \), \( y \), and \( z \) are parallel and cut by a transversal \( w \), various relationships between the angles created by the transversal and the parallel lines can be used to find the measures of unknown angles.

Given that \( m \angle M = 140^\circ \), we can identify the relationships between the angles:

1. **Alternate Interior Angles**: If two alternate interior angles are formed, they are equal.
2. **Corresponding Angles**: Corresponding angles are also equal.
3. **Consecutive Interior Angles**: These angles are supplementary, meaning they add up to \( 180^\circ \).

Without a specific diagram, we'll assume the following:
- Let \( \angle M \) be one of the angles formed at the intersection of transversal \( w \) and one of the parallel lines.
- If \( \angle M = 140^\circ \) is one angle, the angle \( d \) in the same position on the next line (let's say line \( y \)) would also be \( 140^\circ \) due to the corresponding angle theorem.
- The angle \( g \), which is located on the other side of \( w \) in the same transversal direction might be related by being consecutive interior angles.

### Summary:
- If \( \angle d \) is corresponding to \( \angle M \):
\[
m \angle d = 140^\circ
\]

- If \( \angle g \) is a consecutive interior angle to \( \angle M \):
\[
m \angle g = 180^\circ - m \angle M = 180^\circ - 140^\circ = 40^\circ
\]

### Conclusion:
- \( m \angle d = 140^\circ \)
- \( m \angle g = 40^\circ \)

If you have a specific arrangement of angles or a diagram, please provide that for a more tailored response.