In rectangle ABCD, the diagonals intersect at point O, the angle AOD is 70 °. Find the OCD angle.

The diagonal of a rectangle divides it into two equal right-angled triangles. Let’s consider one of them ΔАСD. The angle AOC is a flat angle that is 180 degrees. Based on this:

∠СOD = 180º – ∠АОD;

∠СОD = 180º – 70º = 110º.

The triangle ΔСОD is isosceles, in which the angles ∠ОСD and ∠ОDC are equal as the angles at the base.

Since the sum of all the angles of the triangle is 180º, then:

∠ОСD = (180º – ∠СОD) / 2;

∠ОСD = (180º – 110º) / 2 = 35º.

Answer: the angle ∠СD is 35º.