Question

what are ( mangle f ) and ( mangle i )?
( mangle f = square^circ )
( mangle i = square^circ )

Explanation:

Step1: Recall cyclic quadrilateral property

Opposite angles sum to $180^\circ$.

Step2: Calculate $m\angle F$

$\angle F$ and $\angle H$ are opposite.
$m\angle F = 180^\circ - 81^\circ = 99^\circ$

Step3: Calculate $m\angle I$

$\angle I$ and $\angle G$ are opposite.
$m\angle I = 180^\circ - 80^\circ = 100^\circ$

Answer:

$m\angle F = 99^\circ$
$m\angle I = 100^\circ$