Answer:
1. For quadrilateral ABCD:
AB = AD = 2.7, BC = DC = 3.2, and AC = 3.168
<BAC = <DAC  , <ABC = <ADC =
, <ABC = <ADC =  , and <ACB = <ACD =
, and <ACB = <ACD = 
2. For quadrilateral ABCE:
AB = EC = 2.7, BC = AE = 3.2, and AC = 3.168
<BAC = <ACE  , <ABC = <AEC =
, <ABC = <AEC =  , and <ACB = <EAC =
, and <ACB = <EAC = 
Step-by-step explanation:
Applying the Cosine rule to triangle ABC,
 =
 =  +
 +  - 2/AB/ x /BC/ Cos B
 - 2/AB/ x /BC/ Cos B
           =  +
 +  - 2 x 2.7 x 3.2 Cos 64.3
 - 2 x 2.7 x 3.2 Cos 64.3
          = 7.29 + 10.24 - 17.28 x 0.4337
          = 17.53 - 7.49434
          = 10.03566
AC = 
          = 3.168
Applying the Sine rule,
 =
 =  =
 = 
So that:
 =
 = 
 =
 = 
Sin A = 
          = 
          = 0.9102
⇒ A =  0.9102
 0.9102
        = 
But sum of angles in a triangle is  , so that;
, so that;
A + B + C = 
65.5 + 64.3 + C = 
129.8 + C    = 
C  =  - 129.8
  - 129.8
C = 
1. For quadrilateral ABCD:
AB = AD = 2.7, BC = DC = 3.2, and AC = 3.168
<BAC = <DAC  , <ABC = <ADC =
, <ABC = <ADC =  , and <ACB = <ACD =
, and <ACB = <ACD = 
2. For quadrilateral ABCE:
AB = EC = 2.7, BC = AE = 3.2, and AC = 3.168
<BAC = <ACE  , <ABC = <AEC =
, <ABC = <AEC =  , and <ACB = <EAC =
, and <ACB = <EAC = 