Question

find ( mangle c ), ( moverarc{ab} ), and ( moverarc{cd} ).

Explanation:

Step1: Find $m\angle C$ (cyclic quadrilateral)

In cyclic quadrilaterals, opposite angles sum to $180^\circ$.
$m\angle C = 180^\circ - 68^\circ = 112^\circ$

Step2: Find $m\widehat{AB}$ (inscribed angle theorem)

An inscribed angle is half its intercepted arc.
$m\widehat{AB} = 2 \times m\angle D = 2 \times 68^\circ = 136^\circ$

Step3: Find $m\widehat{CD}$ (total circle is $360^\circ$)

Sum all arcs to $360^\circ$ and solve for $m\widehat{CD}$.
$m\widehat{CD} = 360^\circ - 103^\circ - 136^\circ - 73^\circ = 48^\circ$

Answer:

$m\angle C = 112^\circ$
$m\widehat{AB} = 136^\circ$
$m\widehat{CD} = 48^\circ$