Recall that the diagonals of a rectangle bisect each other and are congruent, therefore:
Substituting the given expression for each segment in the first equation, we get:
Solving the above equation for x, we get:
Substituting x=10 in the equation for segment EI, we get:
Therefore:
Now, to determine the measure of angle IEH, we notice that:
therefore,
Using the facts that the triangles are right triangles and that the interior angles of a triangle add up to 180° we get: