1. the opposite angles of a parallelogram measure(x=30) and (2x-50).Find the measure of each angle of the parallelogram.

2. the ratio of two consecutive angles of a parallelogram is 2:3. find the measurement of the angles of a parallelogram.
3.the difference between the measure of two consecutive angles of a parallelogram is 80. find the measure of each angle of the parallelogram.

1. The opposite angles of a parallelogram are equal

Use that property to form an equation, (you are given the angles) and solve that equation

2. Consecutive angles of a parallelogram add up to 180°. Let the angles be 2x and 3x, form your equation and solve

3. Let one angle be x, then the other angle has to be 180-x
so solve x - (180-x) = 80

(180) because n(180) formula.. :)

To solve these questions, we'll use the properties of parallelograms, which state that opposite angles are congruent and consecutive angles are supplementary.

1. The opposite angles of a parallelogram measure x and 2x - 50. Since opposite angles are congruent, we can set up the equation x = 2x - 50.

Solving the equation:
x = 2x - 50
x - 2x = -50
-x = -50
x = 50

Now that we know the value of x, we can substitute it back into the expression to find the measure of each angle:
Angle 1: x = 50 degrees
Angle 2: 2x - 50 = 2(50) - 50 = 150 - 50 = 100 degrees

Therefore, the measure of each angle of the parallelogram is 50 degrees and 100 degrees.

2. The ratio of two consecutive angles of a parallelogram is given as 2:3. Let the smaller angle be 2x and the larger angle be 3x.

Since consecutive angles are supplementary, we can set up the equation 2x + 3x = 180 degrees.

Solving the equation:
5x = 180
x = 180 / 5
x = 36

Now that we know the value of x, we can substitute it back into the expressions to find the measure of each angle:
Smaller angle: 2x = 2(36) = 72 degrees
Larger angle: 3x = 3(36) = 108 degrees

Therefore, the measure of each angle of the parallelogram is 72 degrees and 108 degrees.

3. The difference between the measure of two consecutive angles of a parallelogram is given as 80 degrees. Let the smaller angle be x and the larger angle be x + 80.

Since consecutive angles are supplementary, we can set up the equation x + (x + 80) = 180 degrees.

Solving the equation:
2x + 80 = 180
2x = 180 - 80
2x = 100
x = 100 / 2
x = 50

Now that we know the value of x, we can substitute it back into the expressions to find the measure of each angle:
Smaller angle: x = 50 degrees
Larger angle: x + 80 = 50 + 80 = 130 degrees

Therefore, the measure of each angle of the parallelogram is 50 degrees and 130 degrees.