Question

lines x,y and z are parallel and are cut by a transversal w given m<a=113 find m<f and m<l

Answer 1

When you have parallel lines cut by a transversal, certain angle relationships hold true:

1. **Corresponding Angles**: If two parallel lines are cut by a transversal, the corresponding angles are equal.
2. **Alternate Interior Angles**: If two parallel lines are cut by a transversal, the alternate interior angles are equal.
3. **Consecutive Interior Angles**: If two parallel lines are cut by a transversal, the consecutive interior angles are supplementary (add up to 180 degrees).

Given that \( m\angle a = 113^\circ \):

1. To find \( m\angle f \):
- If \( \angle f \) is a corresponding angle to \( \angle a \), then \( m\angle f = 113^\circ \).
- If \( \angle f \) is an alternate interior angle to \( \angle a \), then \( m\angle f = 113^\circ \).

(In both cases, \( m\angle f \) is equal to \( m\angle a \)).

2. To find \( m\angle l \):
- If \( \angle l \) is a consecutive interior angle to \( \angle a \), then:
\[
m\angle l = 180^\circ - m\angle a = 180^\circ - 113^\circ = 67^\circ.
\]

In summary:
- If \( \angle f \) is corresponding or alternate interior to \( \angle a \), then \( m\angle f = 113^\circ \).
- If \( \angle l \) is a consecutive interior angle to \( \angle a \), then \( m\angle l = 67^\circ \).