Answer:
Look to the explanation
Step-by-step explanation:
* Lets explain how to solve the problem
- The consecutive integers are the integers after each other like
1 , 2 , 3 , ......
- The rule of the sum of the interior angles of any polygon is:
(n - 2) × 180° , where n is the number of the sides of the polygon
- The sum of the interior angles of a hexagon is equal to the sum of
six consecutive integers
* Lets find the sum of the interior angle of the hexagon
∵ The hexagon has 6 sides
∴ n = 6
∴ The sum of its interior angles = (6 - 2) × 180° = 720°
* Lets find the sum of six consecutive integers
- Assume that the smallest integer is x
∴ The numbers are x , x + 1 , x + 2 , x + 3 , x + 4 , x + 5
∵ Their sum = x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5)
- Add like terms
∴ Their sum = 6x + 15
- Equate the sum of the 6 numbers by the sum of the angles of
the hexagon
∴ 6x + 15 = 720
- Subtract 15 from both sides
∴ 6x = 705
- Divide both sides by 6
∴ x = 117.5
- But 117 .5 not integer
∴ The sum of the interior angles of a hexagon can not equal the
sum of six consecutive integers
- But it can be if the numbers are consecutive odd integers
because the consecutive odd numbers are
x , x + 2 , x + 4 , x + 6 , x + 8 , x + 10
∴ Their sum = 6x + 30
∵ 6x + 30 = 720
- Subtract 30 from both sides
∴ 6x = 690
- Divide both sides by 6
∵ x = 115
∵ x represents the measure of the smallest angle
∴ The measure of the smallest interior angle of the hexagon is 115°
