in the abcd parallelogram ad=10 units ac= 12 units ed= 4.5 units ab= 8 units. If angle aed = 100 then dec= ?

Since ABCD is a parallelogram, we know that opposite sides are equal in length.

Given information:
AD = 10 units
AC = 12 units
ED = 4.5 units
AB = 8 units
∠AED = 100 degrees

To find DEC, we can use the property that opposite angles in a parallelogram are equal.

Step 1: Find ∠ADEC
Since opposite angles in a parallelogram are equal, ∠ADEC = ∠AED = 100 degrees.

Step 2: Find ∠ACD
Since AB and CD are parallel lines and AC is a transversal, ∠ACD is equal to the alternate interior angle with ∠AED.
So, ∠ACD = 180 degrees - ∠AED = 180 degrees - 100 degrees = 80 degrees.

Step 3: Find ∠CED
Since the opposite sides in a parallelogram are equal, AD = BC = 10 units.
AC is the diagonal of ADC, so ADC is an isosceles triangle.

Using the property of isosceles triangles, the base angles are equal.
Therefore, ∠ADC = ∠ACD = 80 degrees.

Using the property that the angles in a triangle add up to 180 degrees,
∠CED = 180 degrees - ∠ADC = 180 degrees - 80 degrees = 100 degrees.

Step 4: Find DEC
DEC is an exterior angle of triangle CED.
DEC = ∠CED + ∠CDE = 100 degrees + 100 degrees = 200 degrees.

Therefore, DEC is equal to 200 degrees.

To find the value of dec, we can use the properties of a parallelogram.

In a parallelgram, opposite sides are equal in length. Therefore, we know that AD = CB = 10 units and AC = BD = 12 units.

We can also use the fact that opposite angles in a parallelogram are congruent. Hence, angle A = angle C and angle B = angle D.

We are given that angle AED = 100 degrees. Since angle A and angle C are congruent, angle AED is also equal to angle CED.

Now, we can use the information to find angle ACD:
angle ACD = angle ACE + angle ECD (Angle Sum of Triangle)

Angle ACE is supplementary to angle AED, so angle ACE = 180 - angle AED = 180 - 100 = 80 degrees.

Thus, angle ACD = angle ACE + angle ECD = 80 degrees + 100 degrees = 180 degrees.

Therefore, dec = 180 degrees.