the convex polygon below has 7 sides. find the value of x.

Explanation:

Step1: Recall sum - of - interior - angles formula

The sum of the interior angles of an $n$-sided polygon is given by $(n - 2)\times180^{\circ}$. For a 7 - sided polygon ($n = 7$), the sum is $(7 - 2)\times180^{\circ}=900^{\circ}$.

Step2: Set up an equation

We know that $106^{\circ}+139^{\circ}+x^{\circ}+147^{\circ}+141^{\circ}+112^{\circ}+129^{\circ}=900^{\circ}$.

Step3: Combine like - terms

$(106 + 139+147+141+112+129)+x=900$. $774 + x=900$.

Step4: Solve for $x$

Subtract 774 from both sides: $x=900 - 774$. $x = 126$.

Answer:

$126$