the convex polygon below has 6 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 6 - sided polygon ($n = 6$), the sum of the interior angles is $(6 - 2)\times180^{\circ}=720^{\circ}$.

Step2: Set up an equation

We know the measures of 5 of the angles: $118^{\circ},103^{\circ},154^{\circ},94^{\circ},121^{\circ}$ and the unknown angle $x$. So, $118 + 103+154 + 94+121+x=720$.

Step3: Simplify the left - hand side

First, add the known angles: $118+103 + 154+94+121=(118+103)+154+(94+121)=221+154 + 215=590$. The equation becomes $590+x = 720$.

Step4: Solve for $x$

Subtract 590 from both sides of the equation: $x=720 - 590$. $x = 130$.

Answer:

$130$