Question

in rhombus abcd, find ( mangle adc ) and ( mangle bcd )? ( mangle adc = square^circ ) ( mangle bcd = square^circ )

Explanation:

Step1: Use rhombus side/angle properties

In a rhombus, opposite sides are parallel, so $AB \parallel DC$. Diagonals bisect the angles, so $\angle 1 = \angle 4$, and $\angle ACD = 61^\circ$ means $\angle BCD = 2 \times 61^\circ$.

Step2: Calculate $m\angle BCD$

$m\angle BCD = 2 \times 61^\circ = 122^\circ$

Step3: Use consecutive angles sum to $180^\circ$

Consecutive angles in a rhombus are supplementary, so $m\angle ADC + m\angle BCD = 180^\circ$

Step4: Solve for $m\angle ADC$

$m\angle ADC = 180^\circ - 122^\circ = 58^\circ$

Answer:

$m\angle ADC = 58^\circ$
$m\angle BCD = 122^\circ$