One of the corners of the rhombus is 20 degrees less than the other corner

One of the corners of the rhombus is 20 degrees less than the other corner of the rhombus. Find the values for the other corners of the rhombus.

Given:

ABCE – rhombus,

angle A = angle B + 20.

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

Solution:

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 B be equal to x degrees, then the degree measure of angle A is equal to x + 20 degrees. We know that the sum of the rhombus degree measures is 360 degrees. Let’s make the equation:

x + x + x + 20 + x + 20 = 360;

4 * x + 40 = 360;

4 * x = 360 – 40;

4 * x = 320;

x = 320: 4;

x = 80 degrees;

80 + 20 = 100 degrees.

Answer: 80 degrees; 80 degrees; 100 degrees; 100 degrees.