Look at this diagram:

Question

C
D
E
F
G
H
I
J

If
DF
and
GI
are parallel lines and mIHE= 112°, what is mGHJ?

Answer 1

To solve for the measure of angle \( mGHJ \) based on the provided information, let's analyze the situation with the given angles and parallel lines.

Since \( DF \) and \( GI \) are parallel lines, and \( mIHE = 112° \), we can apply the concept of corresponding angles and alternate interior angles.

Given the arrangement:

• \( D \) is above \( F \).
• \( G \) is above \( I \).
• \( H \) is an intersection point along with line \( DF \).
• \( E \) is presumably an additional point on line \( GI \).
• \( J \) is another point around the angle we are trying to find.

We know that \( mIHE \) is \( 112° \). Since \( DF \) and \( GI \) are parallel, the angle \( mGHJ \) is an alternate interior angle to \( mIHE \). By the alternate interior angles theorem, we have:

\[ mGHJ = mIHE \]

Thus,

\[ mGHJ = 112° \]

So, the answer is:

\[ \boxed{112°} \]