Thanks for the hint, computer overlord.
Angle FED is a right angle because all angles that subtend diameters are right. So a is complementary to 35°. a=55°.
b is an arc subtended by angle FEP. So its measure will be double that angle, b=70°.
c is subtended by angle DEP which is a. c will be double a, c=110°.
d is subtended by the 60° angle, so d=120°.
e is the other half of the semicircle from d, so together they should make 180°. That means e=60°.
f subtends arc e so will be half, f=30°. Since DEF is right it's also the complementary angle to 60°, also giving f=30°.
g subtends arc b, so it's half its measure, g=35°
h subtends arc d, so its half its measure, h=60°
