the interior angles of a hexagon are 82°, 94°, 109°, x°, 2x° and 3x°. Find the value of x
The sum of the interior angles of a hexagon is given by the formula: (n-2) * 180°, where n is the number of sides of the polygon.
In this case, n = 6 (since it's a hexagon), so the sum of the interior angles is (6-2) * 180° = 4 * 180° = 720°.
The given angles are 82°, 94°, 109°, x°, 2x°, and 3x°.
So we can write an equation to find the value of x:
82° + 94° + 109° + x° + 2x° + 3x° = 720°
Combine like terms:
6x + 285° = 720°
Subtract 285° from both sides:
6x = 720° - 285°
6x = 435°
Divide both sides by 6:
x = 435° / 6
x = 72.5°
Therefore, the value of x is 72.5°.
To find the value of x, we can use the fact that the sum of the interior angles of a hexagon is always equal to 720 degrees.
So, we can sum up the given interior angles:
82° + 94° + 109° + x° + 2x° + 3x° = 720°
Combine like terms:
290° + 6x° = 720°
Subtract 290° from both sides:
6x° = 720° - 290°
6x° = 430°
Divide both sides by 6:
x° = 430° / 6
x° ≈ 71.67°
Therefore, the value of x is approximately 71.67 degrees.