Question

1. quadrilateral efgh is a rhombus. what is $m\angle def$?

$m\angle def =$

Explanation:

Step1: Recall rhombus diagonal properties

Diagonals of a rhombus bisect angles, and adjacent sides are equal. So $EF = EH$, and $\angle EHF = \angle EFH = 32^\circ$.

Step2: Find $\angle FEH$ in $\triangle EFH$

Sum of angles in a triangle is $180^\circ$.
$\angle FEH = 180^\circ - 32^\circ - 32^\circ = 116^\circ$

Step3: Diagonal bisects $\angle FEH$

Diagonal $FH$ bisects $\angle FEH$, so $\angle DEF = \frac{1}{2}\angle FEH$.
$\angle DEF = \frac{116^\circ}{2} = 58^\circ$

Answer:

$58$