Question

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Answer 1

Note: I have already answered this kind of question. https://brainly.in/question/2004618

Given that ratio between an exterior angle and the interior angle = 1:4

We know that measure of an interior angle = (n - 2)(180/n) and the measure of an exterior angle = (360/n).

1/4 = (360/n) / (n - 2)(180/n)

1/4 = (360/n) / n/(n - 2) * 180

1/4 = (360/n) / n(180n - 360)

1/4 = (360)/(180(n - 2))

1/4 = 2/(n - 2)

1(n - 2) = 4 * 2

n - 2 = 8

n = 10.

Therefore the number of sides in the polygon =  10


Hope this helps!