CD-diameter of a circle centered at the point O. BC-chord. The AOC is known to be twice the

CD-diameter of a circle centered at the point O. BC-chord. The AOC is known to be twice the AOD angle. Find the angle AOC and AOD.

Since MB is perpendicular to the plane ABCD, the triangle ABM is rectangular, then tgABM = BM / AB.

BM = AB * tgABM = 20 * tg60 = 20 * √3 cm.

Let’s define the dihedral angle MADB. The AB segment is the projection of the oblique AM, the BD segment is the projection of the oblique DM, then the value of the dihedral angle is equal to the value of the linear angle ABD.

The ABD angle can be determined if the ABCD rhombus, then the ABC angle = 180 – 45 = 135

The diagonals of the rhombus are the bisectors of the angles at its vertices, then the angle ABD = 135/2 = 67.5.

Answer: From point M to the plane 20 * √3 cm, the dihedral angle is 67.50.