# The diagonals of the rhombus make angles with its side, one of which is 40

**The diagonals of the rhombus make angles with its side, one of which is 40 degrees less than the other. What is the smaller angle of the rhombus?**

The rhombus is divided by its diagonals into 4 identical right-angled triangles.

Consider any of these triangles.

According to the condition of the problem, one of the acute angles of such a triangle is 40 ° less than the other.

Let us denote by x the value of the larger angle.

Then the smaller angle should be x – 40 °.

Since the third angle of this triangle is a straight line, we can compose the following equation:

x + x – 40 + 90 = 180,

solving which, we get:

2x + 50 = 180;

2x = 180 – 50;

2x = 130;

x = 130/2 = 65 °.

We find the value of the second angle:

x – 40 = 65 – 40 = 25 °.

Therefore, the smaller angle of the rhombus is 2 8 25 = 50 °.

Answer: 50 °.