The two corners of the rhombus are 1: 3, find the smaller corner of the rhombus.

Given:
quadrangle АВСК – rhombus,
angle A: angle B = 1: 3.
Find the degree measure of the smaller angle of the rhombus, that is, the angle A -?
Solution:
Consider a rhombus ABCK. He has angle A = angle C and angle B = angle K.
Let the angle A = angle C = x degrees, then angle B = angle K = 3 * x degrees. We know that the sum of the degree measures of the angles of a quadrilateral is 360 degrees. Let’s make the equation:
x + x + 3 * x + 3 * x = 360;
x * (1 + 1 + 3 + 3) = 360;
x * 8 = 360;
x = 360: 8;
x = 20 degrees – the degree measure of the angle A.
Answer: 20 degrees.