Question

what are ( mangle s ) and ( mangle t )?( mangle s = square^circ )( mangle t = square^circ )

Explanation:

Step1: Use cyclic quadrilateral property

Opposite angles sum to $180^\circ$.
For $\angle S$:
$m\angle S + m\angle U = 180^\circ$

Step2: Solve for $m\angle S$

Substitute $m\angle U=96^\circ$:
$m\angle S = 180^\circ - 96^\circ = 84^\circ$

Step3: Solve for $m\angle T$

Use same property for $\angle T$:
$m\angle T + m\angle V = 180^\circ$
Substitute $m\angle V=90^\circ$:
$m\angle T = 180^\circ - 90^\circ = 90^\circ$

Answer:

$m\angle S = 84^\circ$
$m\angle T = 90^\circ$