The diagonal of the rhombus makes an angle of 35 ° with its side. Find the degree measure

| February 3, 2021 | education

The diagonal of the rhombus makes an angle of 35 ° with its side. Find the degree measure of the larger of the corners of the rhombus.

The diagonals of the rhombus intersect at right angles and the intersection point is halved.

According to the problem statement, the diagonal of the rhombus forms an angle of 35 ° with one of its sides. Consider a triangle formed by this side of the rhombus and two halves of the diagonals.

This triangle is rectangular (since the diagonals intersect at right angles). This means that the second diagonal of the rhombus together with this side of the rhombus forms an angle of 180 ° – 90 ° – 35 ° = 55 °.

The diagonals of the rhombus divide the corners of the rhombus in half, so the angles of the rhombus mentioned in the conditions of the problem are:

35 ° * 2 = 70 °;

55 ° * 2 = 110 °.

So, the larger of the rhombus angles is 110 °.

Answer: 110 °.



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