Let’s solve the problems step by step based on the image.

Problem 13:

In parallelogram CDEF, if CG = 9, find CE.

• In a parallelogram, the diagonals bisect each other.
  This means that CG = GE.
  Therefore, $CE = CG + GE = 9 + 9 = 18$.
  Answer: $CE = 18$.

Problem 14:

In parallelogram QRST, if RT = 36, find RU.

• Similar to Problem 13, the diagonals of a parallelogram bisect each other.
  Thus, $RU = \frac{RT}{2} = \frac{36}{2} = 18$.
  Answer: $RU = 18$.

Problem 15:

Find the measure of the three missing angles in the rhombus.

• The angles of a rhombus are supplementary when adjacent, and diagonals bisect opposite angles.

• The given angle is $58^\circ$:

  • The opposite angle is also $58^\circ$.
  • The adjacent angles are supplementary to $58^\circ$:
    $180^\circ - 58^\circ = 122^\circ$.

  Answer:
  $x = 58^\circ$,
  $y = 122^\circ$,
  $z = 58^\circ$.

Problem 16:

Find the values of $x$, $y$, and $z$ in the rhombus.

• In a rhombus, opposite angles are equal, and adjacent angles are supplementary.

  • $x + 49 = 90$ (since the rhombus forms a right angle at one diagonal intersection).
    Solve: $x = 90 - 49 = 41$.
  • $y + 6 = 90$.
    Solve: $y = 90 - 6 = 84$.
  • $z - 10 = 90$.
    Solve: $z = 90 + 10 = 100$.

  Answer:
  $x = 41$,
  $y = 84$,
  $z = 100$.

Problem 17:

Find the values of $x$, $y$, and $z$ in the rhombus.

• In a rhombus, adjacent angles are supplementary.

  • Given $10x + 1$ and $59$, we solve:
    $10x + 1 + 59 = 180$.
    $10x + 60 = 180$.
    $10x = 120$.
    $x = 12$.
  • For $2y - 1$:
    $2y - 1 + 59 = 180$.
    $2y + 58 = 180$.
    $2y = 122$.
    $y = 61$.
  • For $z - 7$:
    Opposite angles in a rhombus are equal.
    $z - 7 = 59$.
    $z = 59 + 7 = 66$.

  Answer:
  $x = 12$,
  $y = 61$,
  $z = 66$.

Let me know if you want any part explained further!
Here are five related questions to deepen understanding:

1. What is the key property of diagonals in a rhombus, and how does it differ from that in a parallelogram?
2. How do you calculate angles in a parallelogram if one angle is given?
3. Why are adjacent angles in a rhombus always supplementary?
4. What happens to the diagonal intersection angles if the rhombus is a square?
5. How do you find missing values in a rhombus if only one diagonal length is given?

Tip: Always verify relationships between angles or sides in geometric figures by referring to their defining properties!