Question

the convex polygon below has 7 sides. find the value of x.
(the polygon has angles: 139°, x°, 147°, 141°, 112°, 129°, 106°)

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 $n=7$:
$$(7-2)\times180^\circ = 5\times180^\circ = 900^\circ$$

Step2: Sum known interior angles

Add all given angle measures:
$$106^\circ + 139^\circ + 147^\circ + 141^\circ + 112^\circ + 129^\circ = 774^\circ$$

Step3: Solve for $x$

Subtract the sum of known angles from total interior angles:
$$x = 900^\circ - 774^\circ$$

Answer:

$126^\circ$