Question

use the parallelogram to find $m\angle bad$.
$m\angle bad=\square^\circ$

Explanation:

Step1: Find ∠ADC in △ADC

In $\triangle ADC$, sum of angles is $180^\circ$.
$\angle ADC = 180^\circ - 51^\circ - 33^\circ = 96^\circ$

Step2: Use parallelogram consecutive angles property

In parallelogram $AEDC$, consecutive angles are supplementary.
$\angle BAD + \angle ADC = 180^\circ$

Step3: Calculate ∠BAD

$\angle BAD = 180^\circ - 96^\circ = 84^\circ$
Note: Also, $\angle ADB = \angle BEC = 27^\circ$ (alternate interior angles in parallelogram), so $\angle ADE = 51^\circ + 27^\circ = 78^\circ$, $\angle DAE = 180^\circ - 78^\circ - 18^\circ = 84^\circ$ (verifies the result, as $\angle ACD = 33^\circ$, $\angle ACE = 27^\circ$, so $\angle DCE = 60^\circ$, $\angle AEC = 78^\circ$, $\angle EAD = 180-78-18=84^\circ$)

Answer:

$84$