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 °.
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