Find the angles of the parallelogram if: a) the sum of its two opposite angles is 94 °; b) the difference between two of them is 70 °.

Given:

ABCE – parallelogram,

1) angle A + angle C = 94 degrees,

2) angle A – angle B = 70 degrees.

Find the degree measures of the angles of the parallelogram ABCE: angle A, angle B, angle C, angle E -?

Decision:

Consider a parallelogram ABCE. Its opposite angles are equal to each other, then angle A = angle C, angle B = angle E.

1) angle A = angle C = 94: 2 = 47 degrees.

We know that the sum of the degree measures of a parallelogram is 360 degrees.

Angle B = Angle E = (360 – 94): 2 = 133 degrees.

2) Let the degree measure of angle B be equal to x degrees, then the degree measure of angle A is equal to x + 70 degrees. We know that the sum of the degree measures of a parallelogram is 360 degrees. Let’s make the equation:

x + x + x + 70 + x + 70 = 360;

x + x + x + x + 140 = 360;

4 * x = 360 – 140;

x * 4 = 220;

x = 220: 4;

x = 55 degrees – the degree measure of the angle B;

55 + 70 = 125 degrees is the degree measure of angle A.

Answer: 47 degrees; 47 degrees; 133 degrees; 133 degrees; 2) 55 degrees; 55 degrees; 125 degrees; 125 degrees.