Question

quadrilateral defg is a rhombus. what is m∠gdh? m∠gdh = °

Explanation:

Step1: Recall rhombus properties

In a rhombus, the diagonals are perpendicular bisectors of each other and also bisect the angles of the rhombus.

Step2: Identify right - angled triangle

In rhombus DEFG, the diagonals intersect at H. So, $\angle DHE = 90^{\circ}$.

Step3: Use angle - sum property of triangle

In $\triangle DHE$, we know one angle is $90^{\circ}$ and another is given as $64^{\circ}$. Let $\angle GDH=\angle HDE = x$.
We use the fact that the sum of angles in a triangle is $180^{\circ}$. So in $\triangle DHE$, we have $x + 64^{\circ}+90^{\circ}=180^{\circ}$.

Step4: Solve for $x$

$x=180^{\circ}-(90^{\circ} + 64^{\circ})$.
$x = 26^{\circ}$.

Answer:

$26$