Question

what is m∠fgh? m∠fgh = °

Explanation:

Step1: Identify right - angled triangle

In right - angled triangle EFG, $\angle EFG = 90^{\circ}$.

Step2: Use angle - sum property of a triangle

The sum of angles in $\triangle EFG$ is $180^{\circ}$. Given one angle is $90^{\circ}$ and another $\angle FGE=45^{\circ}$. Let $\angle FEG = x$. Then $x + 90^{\circ}+45^{\circ}=180^{\circ}$, so $x = 45^{\circ}$.

Step3: Consider quadrilateral EFGH

In quadrilateral EFGH, $\angle EHG = 90^{\circ}$, $\angle HEF = 90^{\circ}$ (from right - angled corners). Since $\angle FEG = 45^{\circ}$, and considering the properties of the figure, $\angle FGH=135^{\circ}$. Because the sum of interior angles of a quadrilateral is $360^{\circ}$, and if we know three angles ($90^{\circ},90^{\circ},45^{\circ}$), then $\angle FGH=360^{\circ}-(90^{\circ}+90^{\circ}+45^{\circ}) = 135^{\circ}$.

Answer:

$135$