Question

find ( mangle b ) and ( moverarc{ab} ).
( mangle b = square^circ )
( moverarc{ab} = square^circ )

Explanation:

Step1: Calculate $m\widehat{AB}$

The total degrees in a circle is $360^\circ$. Subtract the given arc measures:
$$m\widehat{AB} = 360^\circ - 122^\circ - 72^\circ - 104^\circ = 62^\circ$$

Step2: Calculate $m\angle B$

In a cyclic quadrilateral, an inscribed angle is half the measure of its intercepted arc. $\angle B$ intercepts $\widehat{ADC}$:
$$m\widehat{ADC} = 122^\circ + 72^\circ = 194^\circ$$
$$m\angle B = \frac{1}{2} \times m\widehat{ADC} = \frac{1}{2} \times 194^\circ = 97^\circ$$

Answer:

$m\angle B = 97^\circ$
$m\widehat{AB} = 62^\circ$