Question

5 rectangle efgh 5 in 32° e h q f g 1 eq = in hf = in m∠feh = ° m∠1 = °

Explanation:

Step1: Use properties of rectangle diagonals

In a rectangle, diagonals are equal and bisect each other. So \(EQ = QG\) and \(QH=QF\), and \(HF = EG\). Given the segment from \(E\) (let's assume the non - diagonal segment related to the angle is part of a congruent setup, but since diagonals bisect each other, if we assume the given \(5\) in segment is related to \(EQ\) (maybe a mis - label, but based on the problem structure), \(EQ = 5\) in.

Step2: Calculate the length of the diagonal \(HF\)

Since diagonals of a rectangle bisect each other, \(HF=2\times EQ\). Substituting \(EQ = 5\) in, we get \(HF = 2\times5=10\) in.

Step3: Find \(m\angle FEH\)

In a rectangle, \(\angle FEH = 90^{\circ}\). Let the angle adjacent to the \(32^{\circ}\) angle (from the non - diagonal line at \(E\)) be \(x\). But if we consider the right - angle of the rectangle, \(m\angle FEH=90^{\circ}\).

Step4: Find \(m\angle1\)

In a rectangle, \(\triangle EHG\) and \(\triangle FGH\) etc. are congruent. Using the angle relationship, if we consider the triangle formed (maybe \(\triangle EHG\) with the given \(32^{\circ}\) angle. Since \(EH\parallel FG\), and using the property that in a rectangle, the diagonals and parallel sides create angle relationships. If we assume the \(32^{\circ}\) angle is related to the non - diagonal line at \(E\), and using the fact that in a rectangle adjacent angles to a right angle and the angle relationships in triangles formed by diagonals. Another approach: In a rectangle, if we consider the triangle formed by the diagonal and sides. Let's use the property that alternate interior angles (if we consider the parallel sides \(EH\) and \(FG\)) and the angle sum in a triangle. Since \(EH\parallel FG\), and the diagonal \(EG\) (or \(HF\)) is a transversal. If we assume the \(32^{\circ}\) angle is \(\angle HEQ\), then in \(\triangle EHG\) (or using the rectangle's angle properties). The measure of \(\angle1 = 32^{\circ}\) (alternate interior angles for \(EH\parallel FG\) and transversal \(HG\) with the angle formed by the diagonal and side).

Answer:

\(EQ = 5\) in, \(HF = 10\) in, \(m\angle FEH=90^{\circ}\), \(m\angle1 = 32^{\circ}\)