Question

calculating measures of isosceles trapezoids. use the diagram to find the missing measures. the measure of angle ghe is. the length of $overline{ge}$ is. f g 15 e $62^{circ}$ 30 h

Explanation:

Step1: Recall properties of isosceles trapezoid

In an isosceles trapezoid, base - angles are equal. Since $\angle FEH = 62^{\circ}$, and $\angle GHE$ and $\angle FEH$ are base - angles of isosceles trapezoid $EFGH$, $\angle GHE=\angle FEH$.
$\angle GHE = 62^{\circ}$

Step2: Recall properties of isosceles trapezoid for side - length

In an isosceles trapezoid, the non - parallel sides are equal. The diagonals of an isosceles trapezoid are equal. Let's assume the trapezoid has some properties related to congruent triangles formed by its diagonals and sides. If we consider the symmetry of the isosceles trapezoid, and assume some congruence relations, we find that the length of $\overline{GE}$ is equal to the length of the other non - parallel side or some related side. Since no other information about non - congruence is given and considering the nature of isosceles trapezoid, if we assume the trapezoid has been constructed in a standard way with given side - lengths and angles, and if we consider the fact that the trapezoid is isosceles, the length of $\overline{GE}$ is equal to the length of the non - parallel side adjacent to the given angle. Here, if we assume the trapezoid has some internal congruence based on its isosceles nature, and since no other side - length information is given to suggest otherwise, the length of $\overline{GE}=15$.

Answer:

The measure of angle $GHE$ is $62^{\circ}$.
The length of $\overline{GE}$ is $15$.