What is the measure of m<JIH ?

FE = 7.5 cm
IJ = 7.5 cm
m < FGE = 28 degrees

A. 124°
B. 56°
C. 28°
D. 62°

To find the measure of ∠JIH, we need to consider the given information:

1. FE = 7.5 cm
2. IJ = 7.5 cm
3. ∠FGE = 28°

Since FE = IJ, we can conclude that triangle FEG is an isosceles triangle, meaning that its base angles are equal. Therefore, ∠EGF = ∠EFG.

Considering that the sum of the angles in a triangle is 180°, we can calculate:

∠EGF + ∠EFG + ∠FGE = 180°

Substituting the given information:

∠EGF + ∠EFG + 28° = 180°

Since ∠EGF = ∠EFG, let's use the letter x to represent both angles:

2x + 28° = 180°

Simplifying the equation:

2x = 180° - 28°
2x = 152°
x = 152° / 2
x = 76°

Since both ∠EGF and ∠EFG are equal to x, each of them equals 76°.

Finally, to find ∠JIH, we can apply the Corresponding Angles Theorem, which states that if two parallel lines are cut by a transversal, then the corresponding angles formed are congruent.

In this case, we can observe that line JI is parallel to line FG, which means that ∠JIH corresponds to ∠EGF.

Therefore, the measure of ∠JIH is equal to the measure of ∠EGF, which is 76°.

So, the correct answer is D. 62°.