a = 133; b = 31; c = 82; d = 64.
Opposite angles in an inscribed quadrilateral are supplementary; this means that d + 116 = 180. Subtracting 116 from both sides, we have d = 64.
By the same theorem, c + 98 = 180; subtracting 98 from both sides, we have c = 82.
Inscribed angles are equal to 1/2 the measure of the intercepted arc. Using this, we have
116 = 1/2(a+99)
Multiplying both sides by 2, we have
232 = a+99
Subtract 99 from both sides:
232 - 99 = a + 99 - 99
133 = a
We also have that
82 = 1/2(133+b)
Multiplying both sides by 2, we have:
164 = 133 + b
Subtract 133 from both sides:
164 - 133 = 133 + b - 133
31 = b
