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 °.
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