Diagonals of rhombus ABCD meet at point O. Find the angles of triangle AOB if angle BCD = 75 °.

Consider first the angles of the rhombus, the angle given in the condition <ВСD = 75 °, and the opposite angle <BAD = 75 ° too.

And the adjacent angle <ABC = <ADC = (180 ° – 75 °) = 105 °.

Now you can consider the angles of the triangle AOB:

<AOB = 90 °, since this is the angle between the diagonals of the rhombus, which is right.

<BAD = 75 °, and the angle <BAO = <DAO, since the diagonals in the rhombus divide the angles of the rhombus into two equal angles. Hence, <ВAO = 75 ° / 2 = 37 ° 30 ‘.

The other angle of this triangle is determined from the equality:

<ABO = 90 ° – 37 ° 30 ‘= 52 ° 30’.