Let
be the measure of the unlabeled arc. Then

The arc with measure
is subtended by a central angle of 180 degrees. We know this because the chord in the picture passes through the circle's center, so it must be the circle's diameter.
So we have

By the inscribed angle theorem, the inscribed angle of measure 36 degrees has half the measure of the central angle subtended by the same arc. This means
.
So
