Answer:
x = 70
Step-by-step explanation:
180* (n-2)
180*(6-2)
180*(4) = 720
102 + 146 + 120 + 124 + 158 = 650
720 - 650 = 70
A polygon is a planar figure characterized by a limited number of straight-line segments. The value of the x is 70°.
A polygon is a planar figure characterized by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.
The sum of the interior angles of a n-sided polygon is calculated using the formula,
Sum of the interior angles = (n-2) × 180°
For the given polygon, the number of sides is equal to 6. Therefore, the sum of the interior angles of the polygon is,
Sum of the interior angles = (6-2) × 180°
= 4 × 180°
= 720°
Further, the sum of the interior angles for the given polygon can be written as,
Sum of the interior angles = 102° + 146° + 120° + 124° + 158° + x°
720° = 102° + 146° + 120° + 124° + 158° + x°
x = 720° - (102° + 146° + 120° + 124° + 158°)
x = 720° - 650°
x = 70°
Hence, the value of the x is 70°.
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