Question

find ( mangle b ).
( mangle b = square^circ )

Explanation:

Step1: Calculate arc AD measure

The total circumference of a circle is $360^\circ$. Subtract the given arc measures:
$$m\overset{\frown}{AD} = 360^\circ - 79^\circ - 65^\circ - 129^\circ = 87^\circ$$

Step2: Apply inscribed angle theorem

The measure of an inscribed angle is half the sum of the measures of its intercepted arcs. $\angle B$ intercepts $\overset{\frown}{AD}$ and $\overset{\frown}{DC}$:
$$m\angle B = \frac{1}{2}(m\overset{\frown}{AD} + m\overset{\frown}{DC})$$

Step3: Substitute values and compute

$$m\angle B = \frac{1}{2}(87^\circ + 129^\circ) = \frac{1}{2}(216^\circ) = 108^\circ$$

Answer:

$108$