Question

find m\\(overset{\frown}{ad}). m\\(overset{\frown}{ad}) = °

Explanation:

Step1: Recall sum of arcs in a circle

The sum of the measures of the arcs of a circle is 360°. Let $m\overset{\frown}{AB}=68^{\circ}$, $m\overset{\frown}{BC} = 88^{\circ}$, and we need to find $m\overset{\frown}{AD}$. Let $m\overset{\frown}{CD}=x$.

Step2: Use property of inscribed - quadrilateral

In an inscribed quadrilateral $ABCD$, the opposite angles are supplementary. But we can also use the arc - sum property. We know that $m\overset{\frown}{AB}+m\overset{\frown}{BC}+m\overset{\frown}{CD}+m\overset{\frown}{AD}=360^{\circ}$.

Step3: Substitute known values

Substitute $m\overset{\frown}{AB} = 68^{\circ}$ and $m\overset{\frown}{BC}=88^{\circ}$ into the equation: $68 + 88+m\overset{\frown}{CD}+m\overset{\frown}{AD}=360$.
We also know that the measure of an inscribed angle is half the measure of its intercepted arc. However, we can directly solve for $m\overset{\frown}{AD}$ from the arc - sum formula.
$m\overset{\frown}{AD}=360-(68 + 88+m\overset{\frown}{CD})$. Since we are not given any information about $m\overset{\frown}{CD}$ and we assume the problem can be solved with the given arc - measures of the non - opposite arcs, we use the fact that the sum of the given non - opposite arcs and the unknown arc must equal 360.
$m\overset{\frown}{AD}=360-(68 + 88)=360 - 156=204^{\circ}$

Answer:

$204$