ABCD rhombus. The diagonals of which intersect at point O. The outer angle of the triangle COB with apex

ABCD rhombus. The diagonals of which intersect at point O. The outer angle of the triangle COB with apex at point B is 130 degrees. Calculate the degree measure of the acute angle of the rhombus.

A rhombus is a quadrilateral in which all sides are equal. In a rhombus, opposite sides are parallel and opposite angles are equal. The sum of all the angles of the rhombus is 360 °. The diagonal of the rhombus divides the angle in half.

From the condition of the problem, the outer angle of the SOV triangle is 130 °, then the adjacent inner angle is 180 – 130 = 50 °. This angle is 1/2 of the obtuse angle of the rhombus ABCD, that is, the angle ABC = 50 * 2 = 100 °.

1. Let’s calculate the degree measure of the acute angle of the rhombus.

(360 – 100 * 2) / 2 = (360 – 200) / 2 = 160/2 = 80 °.

Answer: The degree measure of an acute angle is 80 °.