Question

what are ( mangle g ) and ( mangle h )? ( mangle g = square^circ ) ( mangle h = square^circ )

Explanation:

Step1: Recall cyclic quadrilateral property

In a cyclic quadrilateral, opposite angles sum to $180^\circ$.

Step2: Calculate $m\angle H$

$\angle H$ and $\angle F$ are opposite, so:
$m\angle H = 180^\circ - 111^\circ$
$m\angle H = 69^\circ$

Step3: Calculate $m\angle G$

$\angle G$ and $\angle I$ are opposite, so:
$m\angle G = 180^\circ - 85^\circ$
$m\angle G = 95^\circ$

Answer:

$m\angle G = 95^\circ$
$m\angle H = 69^\circ$