Sure, let's work through this step-by-step.
First, recall that the sum of the interior angles of a polygon with [tex]\( n \)[/tex] sides can be found using the formula:
[tex]\[
\text{Sum of interior angles} = (n-2) \times 180^\circ
\][/tex]
For a pentagon ([tex]\( n = 5 \)[/tex]):
[tex]\[
\text{Sum of interior angles} = (5-2) \times 180^\circ = 3 \times 180^\circ = 540^\circ
\][/tex]
Next, we add up the four given interior angles:
[tex]\[
156^\circ + 72^\circ + 98^\circ + 87^\circ
\][/tex]
Adding these angles step-by-step:
[tex]\[
156^\circ + 72^\circ = 228^\circ
\][/tex]
[tex]\[
228^\circ + 98^\circ = 326^\circ
\][/tex]
[tex]\[
326^\circ + 87^\circ = 413^\circ
\][/tex]
The sum of the given four angles is [tex]\( 413^\circ \)[/tex].
To find the measure of the final interior angle, we subtract the sum of the given angles from the total sum of the interior angles of the pentagon:
[tex]\[
540^\circ - 413^\circ = 127^\circ
\][/tex]
Thus, the measure of the final interior angle is:
[tex]\[
127^\circ
\][/tex]
The correct answer is [tex]\( \boxed{127^\circ} \)[/tex].
