Question

Please help me with my homework

Answer 1

Answer:

$AD = 6$, $DC = 14$, $\angle A = 114^{\circ}$, $\angle B = 66^{\circ}$, $\angle C = 114^{\circ}$

Step-by-step explanation:

From Euclidean Geometry, parallelograms satisfy the following properties:

1) $\angle A = \angle C$, $\angle B = \angle D$

2) $\angle A +\angle D = \angle D + \angle C = \angle C +\angle B = \angle A+\angle B = 180 ^{\circ}$

3) $AD = BC$, $AB = DC$

By 3):

$AD = 6$

By 3):

$DC = 14$

By 2):

$\angle A = 180^{\circ}-\angle D$

$\angle A = 180^{\circ}-66^{\circ}$

$\angle A = 114^{\circ}$

By 1):

$\angle B = 66^{\circ}$

By 1):

$\angle C = 114^{\circ}$