## Answer :

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].