Question

is ↔CE and ↔FH are parallel lines and m<FGI = 46°, what is m<HGD

Answer 1

To find the measure of angle \( m<HGD \), we can use the properties of parallel lines and transversal angles.

Given:
- Lines \( \overleftrightarrow{CE} \) and \( \overleftrightarrow{FH} \) are parallel.
- \( m\angle FGI = 46^\circ \).

Assuming that point \( G \) lies on line \( \overleftrightarrow{FH} \) and line \( \overleftrightarrow{CE} \) is a transversal cutting through them, we can identify the relationship between angles formed.

If angle \( FGI \) and angle \( HGD \) are corresponding angles, alternate interior angles, or same-side interior angles, we can find \( m<HGD \) based on these relationships.

1. **If \( HGD \) is a corresponding angle to \( FGI \)**: Then, \( m<HGD = m<FHI = 46^\circ \).

2. **If \( HGD \) is an alternate interior angle to \( FGI \)**: Then, \( m<HGD = m<FGI = 46^\circ\).

3. **If they are same-side interior angles**: Then, \( m<HGD + m<FGI = 180^\circ\), so \( m<HGD = 180^\circ - 46^\circ = 134^\circ\).

You may need to clarify the exact positions of points \( H \), \( G \), \( F \), and \( I \) in relation to the angles to determine which type of angle relationship exists. However, if they are either corresponding or alternate interior angles, then:

\[
m<HGD = 46^\circ.
\]

If they are same-side interior angles, then:

\[
m<HGD = 134^\circ.
\]