Question

I need assistant with these parallelogram problems​

Answer 1

Problem 6a

1. Angle DCB is supplementary to angle ADC and angle ABC. Reason: Adjacent angles in a parallelogram are always supplementary.
2. AE = EC. Reason: The diagonals of any parallelogram always bisect each other. In other words, the diagonals cut each other in half.
3. DC = AB. Reason: Opposite sides of a parallelogram are congruent.
4. angle DCB = angle DAB. Reason: Opposite angles of a parallelogram are congruent.
5. CD = AB. Reason: segment DC is the same as segment CD. The order of the endpoints does not matter when it comes to listing a segment. Opposite sides of a parallelogram are congruent.

=================================================

Problem 6b

Answers:

angle L = 129

angle S = 51

angle C = 129

----------

Work Shown:

angle U = 51 (given)

angle S = angle U (Opposite angles of a parallelogram are congruent)

L+U = 180 (adjacent angles in parallelogram are supplementary)

L = 180-U

angle L = 180-51

angle L = 129

angle C = angle L (Opposite angles of a parallelogram are congruent)

angle C = 129

=================================================

Problem 6c

Answers:

x = 33/4 = 8.25

y = 50

------------------

Work Shown:

TI across the top is 4x+9

NA across the bottom is 42

TI = NA since opposite sides of a parallelogram are congruent

4x+9 = 42

4x = 42-9

4x = 33

x = 33/4

x = 8.25

------

angle TAN = 3y

angle TIN = 150

angle TAN = angle TIN (opposite angles of parallelogram are congruent)

3y = 150

y = 150/3

y = 50