Question

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

Explanation:

Step1: Recall cyclic quadrilateral rule

Opposite angles sum to $180^\circ$.

Step2: Calculate $m\angle W$

$\angle W$ is opposite $\angle U$, so $m\angle W = 180^\circ - 88^\circ$
$m\angle W = 92^\circ$

Step3: Calculate $m\angle T$

$\angle T$ is opposite $\angle V$, so $m\angle T = 180^\circ - 71^\circ$
$m\angle T = 109^\circ$

Answer:

$m\angle T = 109^\circ$
$m\angle W = 92^\circ$