Question

the convex polygon below has 7 sides. find the value of x.
(the polygon has angles: 92°, 153°, 144°, 142°, x°, 120°, 130°)

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 given interior angles

Add all provided angle measures:
$$92^\circ + 152^\circ + 130^\circ + 128^\circ + 142^\circ + 144^\circ = 888^\circ$$

Step3: Solve for $x$

Subtract the sum of given angles from total interior angles:
$$x = 900^\circ - 888^\circ$$

Answer:

$12^\circ$