F x C 135 D H

The angle FDC is an exterior angle to the triangle FDH. The angle subtended by the arc FH at the center F is x. The angle subtended by the arc FH at the circumference D is 135 degrees. This is incorrect as an angle at the circumference should be less than 180 degrees and subtended by the minor arc. Assuming 135 degrees is the angle between the secant FD and the tangent DH, and also the angle subtended by the arc H at the circumference. The angle subtended by the arc H at the center F is x. The angle subtended by the arc H at the circumference D is 135 degrees. This implies that the angle subtended by the major arc H at the circumference is 135 degrees. Therefore, the angle subtended by the minor arc H at the circumference is 180 - 135 = 45 degrees. The angle at the center is twice the angle at the circumference. So, x = 2 * 45 = 90 degrees.