Find all the angles of the parallelogram if the difference between two of them is: 1) 70 °, 2) 110 °, 3) 140 °

Let’s take advantage of the fact that the sum of the angles of the parallelogram adjacent to one side is 180 °.

Let us denote by x and y the angles of the parallelogram adjacent to one side, and x will be a large angle, and y – correspondingly smaller.

Then we can write the following relation:

x + y = 180.

1) By the condition of the problem, x – y = 70.

We solve the system of equations:

x + y = 180;

x – y = 70.

Adding the first equation with the second, we get:

x + y + x – y = 180 + 70;

2x = 250;

x = 250/2;

x = 125 °.

Substituting the found value x = 125 into the equation x + y = 180, we get:

125 + y = 180:

y = 180 – 125;

y = 55 °.

Therefore, in this case, the smaller parallelogram angles are 55 ° and the larger parallelogram angles are 125 °.

2) By the condition of the problem, x – y = 110.

We solve the system of equations:

x + y = 180;

x – y = 110.

Adding the first equation with the second, we get:

x + y + x – y = 180 + 110;

2x = 290;

x = 290/2;

x = 145 °.

Substituting the found value x = 145 into the equation x + y = 180, we get:

145 + y = 180:

y = 180 – 145;

y = 35 °.

Therefore, in this case, the smaller parallelogram angles are 35 ° and the larger parallelogram angles are 145 °.

3) By the condition of the problem, x – y = 140.

We solve the system of equations:

x + y = 180;

x – y = 140.

Adding the first equation with the second, we get:

x + y + x – y = 180 + 140;

2x = 320;

x = 320/2;

x = 160 °.

Substituting the found value x = 160 into the equation x + y = 180, we get:

160 + y = 180:

y = 180 – 160;

y = 20 °.

Therefore, in this case, the smaller parallelogram angles are 20 ° and the larger parallelogram angles are 160 °.