Question

find the angle measure of $\angle dce$ in the rhombus below if $m\angle adc = 76^{\circ}$.
$m\angle dce = $ write your answer here

Explanation:

Step1: Find adjacent rhombus angle

In a rhombus, consecutive angles are supplementary.
$m\angle BCD = 180^\circ - m\angle ADC = 180^\circ - 76^\circ = 104^\circ$

Step2: Bisect angle with rhombus diagonal

Rhombus diagonals bisect interior angles.
$m\angle DCE = \frac{1}{2}m\angle BCD = \frac{1}{2} \times 104^\circ$

Answer:

$52^\circ$