Question

use the parallelogram to find m∠bad.
m∠bad = 102°

Explanation:

Step1: Find $\angle ADC$

$\angle ADC = 51^\circ + 33^\circ = 84^\circ$

Step2: Find $\angle ACD$

$\angle ACD = 27^\circ$

Step3: Calculate $\angle CAD$

In $\triangle ADC$, $\angle CAD = 180^\circ - 84^\circ - 27^\circ = 69^\circ$

Step4: Find $\angle ADB$

$\angle ADB = \angle DCE = 27^\circ$ (alternate interior angles)

Step5: Calculate $\angle BAC$

$\angle BAC = \angle ADB = 27^\circ$ (alternate interior angles)

Step6: Sum to find $\angle BAD$

$\angle BAD = \angle CAD + \angle BAC = 69^\circ + 33^\circ = 102^\circ$

Answer:

$102^\circ$