Look at this diagram:

Question

C
D
E
F
G
H
I
J




























If
DF
and
GI
are parallel lines and
m
DEC
= 115°, what is
m
GHE
?

Answer 1

To find the measure of angle \( mGHE \), we first need to analyze the relationship between the angles given that lines \( DF \) and \( GI \) are parallel.

Since \( DF \) and \( GI \) are parallel lines and \( D \) and \( G \) are points connected to \( C \) and \( H \) respectively, we can identify other angles based on the transversal that crosses the parallel lines.

Given \( mDEC = 115^\circ \) as an angle formed by \( DC \) traversing the parallel lines \( DF \) and \( GI \), the angle \( mGHE \) can be determined using the concept of corresponding angles.

Here, angle \( DEC \) and angle \( GHE \) are corresponding angles because they are both formed on the same side of the transversal and between the two parallel lines.

Since corresponding angles are equal when two lines are parallel, we can conclude:

\[ mGHE = mDEC = 115^\circ. \]

Thus, the measure of angle \( mGHE \) is:

\[ \boxed{115^\circ}. \]