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professor190 [17]
3 years ago
15

if the sum of the measures of the interior angles of a polygon is twice the sum of its exterior angles, how many sides does it h

ave?
Mathematics
1 answer:
Valentin [98]3 years ago
4 0

Answer:

6

Step-by-step explanation:

The sum of the exterior angles of any polygon = 360°

Thus the sum of the interior angles = 2 × 360° = 720°

The sum of the interior angles of a polygon = 180° (n - 2), hence

180(n - 2) = 720 ← divide both sides by 180

n - 2 = 4 ← add 2 to both sides

n = 6

The polygon has 6 sides

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Answer:

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Step-by-step explanation:

Given the sequence

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a_n=a_1+\left(n-1\right)d

Here,

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computing the differences of all the adjacent terms

d = 15a-12a = 3a, d = 18a-15a=3a, d=21a-18a=3a, d=24a-21a=3a

using the nth term formula

a_n=a_1+\left(n-1\right)d

substituting a₁ = 12a, d = 3a

a_n=12a+\left(n-1\right)3a

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Therefore, the general rule for the nth term of this sequence will be:

a_n=3na+9a

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