Answer:
EG = 34
m∠IHE = 53°
Explanation:
∠IHE corresponds to ∠IEH so their measurements are equal. Because EG and FH are diagonals, EI and FI are of equal length; similarly EG is double the length of EI.
EI = FI
2x + 7 = 6x - 13
-4x = -20
x = 5
EG = 2(EI)
= 2(2x + 7)
= 2(2(5) + 7)
= 2(17)
= 34
EG and FH are diagonals of rectangle EFGH. The diagonals of the rectangle don't necessarily create a 90° angle because we're looking at a rectangle. But ∠IEF and ∠IEH are complementary angles because they form a 90° angle.
m∠IHE + m∠IEF = 90°
m∠IHE + 37° = 90°
m∠IHE = 53°