1. **State the problem:** We have a quadrilateral with angles labeled as follows: top-left angle is $10x - 6$ degrees, top-right angle is 109 degrees, bottom-right angle is 79 degrees, and bottom-left angle is $20x - 2$ degrees. We need to find the value of $x$. 2. **Formula and rule:** The sum of the interior angles of any quadrilateral is always 360 degrees. So, $$ (10x - 6) + 109 + 79 + (20x - 2) = 360 $$ 3. **Combine like terms:** $$ 10x - 6 + 109 + 79 + 20x - 2 = 360 $$ $$ (10x + 20x) + (-6 + 109 + 79 - 2) = 360 $$ $$ 30x + 180 = 360 $$ 4. **Isolate $x$:** $$ 30x + 180 = 360 $$ $$ 30x = 360 - 180 $$ $$ 30x = 180 $$ 5. **Solve for $x$:** $$ x = \frac{180}{30} $$ $$ x = 6 $$ 6. **Answer:** The value of $x$ is **6**.