The side of the rhombus forms angles with its diagonals, the difference of which is 15 degrees. Find the corners of the diamond.

The diagonals of the rhombus are the bisectors of its catch and divide them in half. Based on this:

∠В = ∠ABO · 2;

∠A = ∠BAO · 2.

Thus, four equal right-angled triangles are formed.

Consider the triangle ΔABO.

Since the angle ∠ABO is 15 ° less than the angle ∠BAO, then we express:

x – degree measure ∠ABO;

x + 15 ° – the degree measure of the angle ∠BAO;

x + x + 15 + 90 = 180;

x + x = 180 – 90 – 15;

2x = 75;

x = 75/2 = 37.5;

∠ABO = 37.5 °;

∠BAO = 37.5 ° + 15 ° = 52.5 °;

∠В = 37.5 ° 2 = 75 °;

∠А = 52.5 ° 2 = 105 °.

Answer: The angles of the rhombus are 75 ° and 105 °.