Question

what are ( mangle r ) and ( mangle u )?
( mangle r = square^circ )
( mangle u = square^circ )

Explanation:

Step1: Use cyclic quadrilateral property

In a cyclic quadrilateral, opposite angles sum to $180^\circ$. For $\angle R$ and $\angle T$:
$m\angle R + m\angle T = 180^\circ$

Step2: Solve for $m\angle R$

Substitute $m\angle T=104^\circ$:
$m\angle R = 180^\circ - 104^\circ$
$m\angle R = 76^\circ$

Step3: Solve for $m\angle U$

Use the same property for $\angle U$ and $\angle S$:
$m\angle U + m\angle S = 180^\circ$
Substitute $m\angle S=87^\circ$:
$m\angle U = 180^\circ - 87^\circ$
$m\angle U = 93^\circ$

Answer:

$m\angle R = 76^\circ$
$m\angle U = 93^\circ$