The diagonals of rectangle ABCD meet at point O. Find the angle ABD if it is 30 degrees greater than the angle COD.

Since the ABCD figure is a rectangle, then its diagonals create the same opposite corners. Thus, the COD angle is equal to the AOB angle, and the ABD angle is equal to the CAB angle. A triangle AOB has formed, in which the angle ABO (aka the desired ABD) is 30 ° more than AOB.

Since all the angles of the triangle are 180 °, we find them using the equation, where X is the value of the angle AOB, and (30 + X) is the value of ABO and BAO:

X + 30 + X + 30 + X = 180

3X = 120

X = 40

30 + 40 = 70

Answer: angle ABD 70 °