Question
is CE↔ and FH↔ are parallel lines and m<CDB = 136°, what is m <EDG?
Answers
Answered by
GPT-4o mini
To determine the measure of angle \( \angle EDG \) given that lines \( CE \) and \( FH \) are parallel and \( m \angle CDB = 136^\circ \), we can use the properties of parallel lines and transversals.
Since \( CE \) and \( FH \) are parallel, the angles formed on the same side of the transversal \( CD \) must be supplementary. Thus, we have:
\[
m \angle CDB + m \angle EDG = 180^\circ
\]
Substituting the given value of \( m \angle CDB \):
\[
136^\circ + m \angle EDG = 180^\circ
\]
To find \( m \angle EDG \), we can rearrange this equation:
\[
m \angle EDG = 180^\circ - 136^\circ
\]
Calculating that gives:
\[
m \angle EDG = 44^\circ
\]
Therefore, the measure of angle \( \angle EDG \) is \( 44^\circ \).
Since \( CE \) and \( FH \) are parallel, the angles formed on the same side of the transversal \( CD \) must be supplementary. Thus, we have:
\[
m \angle CDB + m \angle EDG = 180^\circ
\]
Substituting the given value of \( m \angle CDB \):
\[
136^\circ + m \angle EDG = 180^\circ
\]
To find \( m \angle EDG \), we can rearrange this equation:
\[
m \angle EDG = 180^\circ - 136^\circ
\]
Calculating that gives:
\[
m \angle EDG = 44^\circ
\]
Therefore, the measure of angle \( \angle EDG \) is \( 44^\circ \).
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