the convex polygon below has 8 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 an $n = 8$ - sided polygon, the sum of interior angles is $(8 - 2)\times180^{\circ}=6\times180^{\circ}=1080^{\circ}$.

Step2: Set up an equation

We know that $127+140 + 118+153+156+117+134+x=1080$.

Step3: Simplify the left - hand side

$(127+140)+(118+153)+(156+117)+(134+x)=1080$. $267+271+273+134+x = 1080$. $(267+271)+273+134+x=1080$. $538+273+134+x = 1080$. $(538+273)+134+x=1080$. $811+134+x = 1080$. $945+x = 1080$.

Step4: Solve for $x$

Subtract 945 from both sides of the equation: $x=1080 - 945$. $x = 135$.

Answer:

$135$