Diagonals break a rhombus into 4 triangles. Find the angles of these triangles if one of the angles is 150 degrees.

An angle of 150 degrees is an obtuse angle, let the angle A = 150 degrees.

We use the property of the diagonals of the rhombus, which intersect at an angle of 90 degrees, are halved at the point of intersection and are the bisectors of its corners.

We use the property of opposite angles that are equal to each other.

In a diamond, the adjacent angles add up to 180 degrees. Hence the angle B = 180 – A = 180 – 150 = 30 (degrees).

Consider a triangle ABO: angle AAO = 1/2 A = 1/2 * 150 = 75 (degrees);

angle AOB = 90 (degrees) by the property of the diagonals;

angle ABO = 1/2 B = 1/2 * 30 = 15 (degrees).

The triangles into which the diagonals of the rhombus are divided are equal to each other, therefore their corresponding angles are equal.