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Vladimir [108]
3 years ago
10

The sum of the interior angles of a hexagon is equal to the sum of six consecutive integers. What is the measure of the smallest

angle of the hexagon?​
Mathematics
1 answer:
Dmitrij [34]3 years ago
4 0
The sum of the interior angles of a hexagon is equal to sum of six consecutive numbers. Hence let the smallest consecutive number be x. Then other five numbers are x+1, x+2, x+3,x+4 and x+5. Hence the measure of the smallest angle is 117.5 cm.
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Obviously 1 < 9.

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Taking another look at x+3<9, subtract 3 from both sides.  Then x<6.
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Shade the area between these two vertical lines to obtain the desired graph.
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Answer: The numbers are 1 and 3.

Step-by-step explanation:

Let x = smaller number , y= larger number.

As per given,

x=\dfrac{y}{3}   ...(i)

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Put value of x from (i) in (ii)

\dfrac{y}{3}+y=y^2-5\\\\\Rightarrow\ \dfrac43y=y^2-5\\\\\Rightarrow\ 3y^2-4y-15=0\\\\\Rightarrow\ 3y^2-9y+5y-15=0\\\\\Rightarrow\ 3y(y-3)+5(y-3)=0\\\\\Rightarrow\ (y-3)(3y+5)=0\\\\\Rightarrow\ y=3 \ \ or\ y=\dfrac{-5}{3}

Since numbers are positive , so y=3 is correct.

And x will be 1  [from (i)]

Hence, the numbers are 1 and 3.

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olganol [36]

Answer:

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Step-by-step explanation:

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3 years ago
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Answer:

the answer would be number 2

Step-by-step explanation:

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