Look at this diagram:

Question

C
D
E
F
G
H
I
J

If
DF
and
GI
are parallel lines and mIHJ= 115°, what is mIHE?

Answer 1

To solve for \( mIHE \) given the parallel lines \( DF \) and \( GI \) and the angle \( mIHJ = 115^\circ \), we can use the properties of parallel lines and transversals.

Since \( DF \) is parallel to \( GI \), the angles formed between the two lines when intersected by a transversal must maintain certain relationships. The angle \( mIHJ \) is an exterior angle formed by the transversal line \( IH \).

Since \( mIHJ \) and \( mIHE \) are corresponding angles (with \( IH \) acting as a transversal that crosses both \( DF \) and \( GI \)), we know that corresponding angles are congruent when formed by a transversal cutting through two parallel lines.

Thus, we find:

\[ mIHE = mIHJ = 115^\circ \]

Therefore, \( mIHE = 115^\circ \).