To find the measure of the third angle in a triangle, we can use the fact that the sum of the angles in any triangle is always $180^\circ$.

Given angles:

1. $63^\circ 59'$
2. $108^\circ 11'$

Let's first add these two angles together:

$63^\circ 59' + 108^\circ 11' = 172^\circ 70'$

Since $70'$ is equivalent to $1^\circ 10'$, the sum becomes:

$172^\circ 70' = 173^\circ 10'$

Now, subtract this sum from $180^\circ$ to find the third angle:

$180^\circ - 173^\circ 10' = 6^\circ 50'$

Since the question asks for a whole number:

$\text{The measure of the third angle is } 7^\circ.$

Would you like more details or have any questions?

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1. How do you calculate the sum of angles in a triangle?
2. What is the importance of angle sum property in triangles?
3. Can a triangle have more than one obtuse angle?
4. How would you handle non-standard angle measurements (like degrees and minutes)?
5. Why do the angles in a triangle always add up to 180 degrees?

Tip: When dealing with angles in degrees and minutes, remember that 60 minutes ($60'$) make 1 degree ($1^\circ$).