Two chords AB and CD are drawn in the circle, intersecting at point M.

Two chords AB and CD are drawn in the circle, intersecting at point M. Find the angle AMD if the arc AD is 70 degrees and the arc BC is 10 degrees.

Let’s draw the chords AC and BD.

The inscribed angle BAC rests on the СВ arc and is equal to half of its degree arc. Angle BAC = 10/2 = 50.

The inscribed angle ACD rests on the arc AD and is equal to half of its degree arc. Angle АСD = 70/2 = 35.

In the AСO triangle, the angle AOC = (180 – СAO – AСO) = (180 – 5 – 35) = 140.

The AOC angle is adjacent to the AOD angle, then the AOD angle = (180 – AOC) = (180 – 140) = 40.

Answer: Angle AOD is 40.