the convex polygon below has 5 sides. find the value of x.

Explanation:

Step1: Recall sum - of - interior - angles formula

The sum of interior angles of an $n$-sided polygon is given by $(n - 2)\times180^{\circ}$. For a 5 - sided polygon ($n = 5$), the sum is $(5 - 2)\times180^{\circ}=540^{\circ}$.

Step2: Set up an equation

We know the sum of the given angles and $x$ is equal to the sum of interior angles of the pentagon. So, $129^{\circ}+82^{\circ}+121^{\circ}+147^{\circ}+x^{\circ}=540^{\circ}$.

Step3: Simplify the left - hand side

$129 + 82+121 + 147+x=479 + x$.

Step4: Solve for $x$

Set $479 + x=540$. Then $x=540 - 479$. So, $x = 61$.

Answer:

$61$