use the polygon sum to solve for x.

Explanation:

Step1: Recall the polygon sum formula

The sum of interior angles of a quadrilateral ((n = 4)) is ((n - 2)\times180^{\circ}=(4 - 2)\times180^{\circ}=360^{\circ}).

Step2: Set up the equation

Let the unknown angle be (x). Then (x+110^{\circ}+79^{\circ}+55^{\circ}=360^{\circ}).

Step3: Solve for (x)

First, add the known angles: (110 + 79+55=244). Then (x=360 - 244).

Answer:

(x = 116^{\circ})