The diagonals of rectangle ABCD meet at point M, the angle BMC is 120 °. what is the angle MAD?

The intersection of the diagonals in the rectangle halves the diagonals. This means that all four triangles formed by the diagonals are isosceles (with two equal sides).

The vertical angles at the intersection of two straight lines are equal. The corners of the IUD and AMD are vertical:

∠ BMC = ∠ AMD = 120 °;

The AMD triangle is isosceles with equal sides AM and MD and base AD. In an isosceles triangle, the angles at the base are equal, which means:

∠ MAD = ∠ MDA;

The sum of all angles in a triangle is 180 °. Means:

(∠ MAD + ∠ MDA) = 180 ° – ∠ AMD;

(∠ MAD + ∠ MDA) = 180 ° – 120 °;

(∠ MAD + ∠ MDA) = 60 °;

∠ MAD = 60 ° / 2;

∠ MAD = 30 °.

Answer: 30 °