Question

Given m, is parallel to, nm∥n, find the value of x.
m
n
t
103°
x°
Answer
x =

Answer 1

To solve for \( x \) given that lines \( m \) and \( n \) are parallel (i.e., \( m \parallel n \)) and the angles formed are \( 103^\circ \) and \( x^\circ \), we can utilize the properties of parallel lines and the angles formed by a transversal.

When a transversal crosses parallel lines, several pairs of angles are formed. Specifically, corresponding angles, alternate interior angles, and consecutive interior angles come into play. Based on the angle you provided (103°), we need to know how it relates to \( x \).

Assuming \( 103^\circ \) is either:

1. **An interior angle**, which pairs with a corresponding angle on line \( n \):

\[
x = 103^\circ
\]

2. **An alternate interior angle** with respect to \( x \):

If \( x \) is the alternate interior angle to \( 103^\circ \):

\[
x = 103^\circ
\]

3. **A consecutive interior angle** with respect to \( x \):

If \( 103^\circ \) is a consecutive interior angle with \( x \):

\[
x + 103^\circ = 180^\circ
\]

Solving for \( x \):

\[
x = 180^\circ - 103^\circ = 77^\circ
\]

Without further information, if \( 103^\circ \) were a corresponding or alternate interior angle, then \( x \) would equal \( 103^\circ \). If \( 103^\circ \) is a consecutive interior angle, then \( x \) would equal \( 77^\circ \).

Thus, the answer can be:

- If \( 103^\circ \) is either a corresponding or alternate interior angle:
- \( x = 103^\circ \)

- If \( 103^\circ \) is a consecutive interior angle:
- \( x = 77^\circ \)

Please specify which relationships apply if more context is available.