find $m\\widehat{cd}$. $m\\widehat{cd} = \\square ^\\circ$

Explanation:

Step1: Recall total circle degrees

A full circle is $360^\circ$.

Step2: Find arc BC measure

Use inscribed angle theorem: inscribed $\angle D = 89^\circ$, so arc $AB +$ arc $BC = 2\times89^\circ = 178^\circ$. We know arc $AB=141^\circ$, so arc $BC = 178^\circ - 141^\circ = 37^\circ$.

Step3: Calculate arc CD

Subtract known arcs from $360^\circ$: $$m\overset{\frown}{CD}=360^\circ - 95^\circ - 141^\circ - 37^\circ$$ $$m\overset{\frown}{CD}=87^\circ$$

Answer:

$87$