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’.
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