Question

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 of interior angles is $(7 - 2)\times180^{\circ}=900^{\circ}$.

Step2: Set up an equation

We know that the sum of the given angles and $x$ is equal to the sum of the interior angles of the 7 - sided polygon. So, $x+112 + 142+143+105+141+125 = 900$.

Step3: Simplify the left - hand side of the equation

First, add the known angles: $112+142+143+105+141+125 = 768$. Then the equation becomes $x + 768=900$.

Step4: Solve for $x$

Subtract 768 from both sides of the equation: $x=900 - 768$. So, $x = 132$.

Answer:

$132$