Question

1. find ( mangle dhg ).

Explanation:

Step1: Set angles equal (rectangle property)

In a rectangle, opposite angles formed by diagonals are equal, so $\angle DEG = \angle GFD$.
$$9x + 3 = 14x - 27$$

Step2: Solve for x

Rearrange terms to isolate x.
$$3 + 27 = 14x - 9x$$
$$30 = 5x$$
$$x = \frac{30}{5} = 6$$

Step3: Find $\angle DEG$

Substitute x into $\angle DEG$ expression.
$$m\angle DEG = 9(6) + 3 = 57^\circ$$

Step4: Find $\angle DHG$

$\angle DHG$ is supplementary to $\angle DHE$, and $\angle DHE = 180^\circ - 2\times57^\circ$. So:
$$m\angle DHG = 2\times57^\circ = 114^\circ$$

Answer:

$114^\circ$