Parallelogram and its properties:
A parallelogram is a four-sided polygon in which opposite sides are parallel. It has several important properties:

1. Opposite sides are equal in length.
2. Opposite angles are equal in measure.
3. Consecutive angles are supplementary (their sum is 180 degrees).
4. The diagonals bisect each other.

Given:
In parallelogram PQRS, we are given the measures of angle P and angle Q as follows:
Angle P = 3x - 5
Angle Q = 2x + 15

Finding the measures of all angles:
To find the measures of all angles in parallelogram PQRS, we can use the properties mentioned above.

1. Opposite angles are equal:
- Angle P is opposite to angle R, so they have equal measures.
- Angle Q is opposite to angle S, so they have equal measures.

2. Consecutive angles are supplementary:
- Angle P and angle Q are consecutive angles, so their sum is 180 degrees.
- Angle R and angle S are also consecutive angles, so their sum is 180 degrees.

Applying the properties:
1. Opposite angles are equal:
- Angle P = Angle R (both represent the same angle in different notations)
- Angle Q = Angle S (both represent the same angle in different notations)

2. Consecutive angles are supplementary:
- Angle P + Angle Q = 180 degrees
(3x - 5) + (2x + 15) = 180
5x + 10 = 180
5x = 170
x = 34

- Angle R + Angle S = 180 degrees
(3x - 5) + (2x + 15) = 180
5x + 10 = 180
5x = 170
x = 34

Calculating the measures of all angles:
We can substitute the value of x (which we found as 34) into the given expressions for angle P and angle Q to calculate their measures. Then, using the properties mentioned above, we can find the measures of angles R and S.

- Angle P = 3x - 5 = 3(34) - 5 = 97 degrees
- Angle Q = 2x + 15 = 2(34) + 15 = 83 degrees
- Angle R = Angle P = 97 degrees
- Angle S = Angle Q = 83 degrees

Therefore, the measures of all angles in parallelogram PQRS are as follows:
- Angle P = 97 degrees
- Angle Q = 83 degrees
- Angle R = 97 degrees
- Angle S = 83 degrees