Question

the convex polygon below has 8 sides. find the value of x.
140°
118°
127°
153°
x =
134°
x°
135°
117°

Explanation:

Step1: Calculate total interior angles

The formula for the sum of interior angles of an n-sided polygon is $(n-2)\times180^\circ$. For $n=8$:
$$(8-2)\times180^\circ = 6\times180^\circ = 1080^\circ$$

Step2: Sum given interior angles

Add all provided angle measures:
$$140+118+153+117+135+134+127 = 1024$$

Step3: Solve for $x$

Subtract the sum of given angles from the total interior angle sum:
$$x = 1080 - 1024$$

Answer:

$x = 56$