Find the corners of a rhombus in which the angles are 7: 9.

Given:

ABCE – rhombus,

angle A: angle B = 5: 7.

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

Decision:

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

Let the degree measure of angle A be 5 * x degrees, then the degree measure of angle B is 7 * x degrees. We know that the sum of the degree measures of a parallelogram is 360 degrees. Let’s make the equation:

5 * x + 5 * x + 7 * x + 7 * x = 360;

x * (5 + 5 + 7 + 7) = 360;

x * 24 = 360;

x = 360: 24;

x = 15 degrees;

15 * 5 = 75 degrees – the degree measure of the angle A;

15 * 7 = 105 degrees – the degree measure of angle B.

Answer: 75 degrees; 105 degrees; 75 degrees; 105 degrees.