Step-by-step explanation:
We will use parallelogram properties to answer our given problems.
(1) Since we know that opposite sides of parallelogram are congruent, therefore measure of side MN and side KN will be equal to the measure of their opposite sides.
LM=KN and KL=MN
Upon substituting our given values we will get,
45=KN and 31=MN
Property: The opposite angles of parallelogram are congruent and consecutive angles are supplementary.
We have been given , therefore
.
We will find measure of angle K by using supplementary angles.
By opposite angles of parallelogram .
(2) Opposite sides of parallelogram are equal. Therefore, CF=DE and FE=CD.
Upon substituting our given values we will get,
CF=10 and FE=15.
Property: Diagonals of parallelogram bisect each other.
So CE will be 2 times CG and GD will be half the length of FD.
(3) Property: Opposite sides of parallelogram are congruent.
and
Upon substituting our given values we will get,
and
Property: Diagonals of parallelogram bisect each other.
So SQ will be 2 times TQ and PT will be half the length of PR.
Property: The opposite angles of parallelogram are congruent and consecutive angles are supplementary.
Alternate interior angles.
Opposite angles of parallelogram.
Therefore, measure of angle QRS will 74 degrees.
Alternate interior angles.
Now let us find measure of angle PSQ.
The image is not clear, so I am unable to answer the last two problems.