From the top of the obtuse angle of the rhombus, heights are drawn that form an angle of 40 °.

From the top of the obtuse angle of the rhombus, heights are drawn that form an angle of 40 °. Calculate the angles of the rhombus.

Two heights, which are drawn, according to the conditions of this problem, from the vertex of an obtuse angle, form a convex quadrilateral (the sum of the angles is 360 °).

Let’s calculate how many degrees the obtuse angle of this quadrangle (aka the obtuse angle of the rhombus) equals, if we know, according to the conditions from this problem, that the heights form an angle of 40 °:

360 – 2 * 90 – 40 = 140.

Let’s calculate how many degrees each of the acute angles of this rhombus is equal to:

180 – 140 = 40.

Answer: Sharp angles at 40 °, obtuse at 140 °.