Question

The interior angle is (13x+17)°.
The exterior angle is (8x+16)°.
How many sides does the polygon have?

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Answer 1

Answer:

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Step-by-step explanation:

n is the number of sides

The exterior angle is given by 360 / n

The interior angle is given by (n-2)x180 / n

If the interior is 8x bigger than the exterior then:

360 x 8 / n = (n-2) x 180 / n

360 x 8 = (n-2) x 180 [removing the /n from both sides]

180 x 2 x 8 = (n-2) x 180

16 = n-2 [removing the x180 from both sides]

n = 16+2 = 18

Therefore it is an 18 sided polygon.