Find the acute angle of the rhombus if you know that the diagonal makes an angle with the side

Find the acute angle of the rhombus if you know that the diagonal makes an angle with the side of the angle, which is equal to 35 degrees.

The diagonals of the rhombus intersect at right angles and the intersection point is halved. They are also the bisectors of the angles from which they come out (that is, they divide them in half).

Thus:

∠A = ∠BAO · 2;

∠А = 35 ° 2 = 70 °.

Since the opposite angles of the rhombus are equal to each other, then:

∠А = ∠С = 70 °.

Since the sum of the degree measures of all angles is 360 °, then:

∠В = ∠Д = (360 ° – ∠А – ∠С) / 2;

∠В = ∠Д = (360 ° – 70 ° – 70 °) / 2 = 220 ° / 2 = 110 °.

Answer: The acute angle of the rhombus is 70 °.